Trajectory validation for autonomous driving

ABSTRACT

A method of determining whether a planned trajectory of a first vehicle over a road along which the first vehicle and a second vehicle are traveling, is invalid, comprising: obtaining the planned trajectory, comprising a first state of the first vehicle for each of a plurality of time instants; obtaining a second state of the second vehicle for each time instant; determining, for each time instant, a respective lateral range extending from the second vehicle; and determining that the planned trajectory is invalid where, for the first and second states at one or more of the time instants: the first vehicle is within the lateral range and within a lane boundary region of the road; and a direction of a lateral velocity of the first vehicle is towards the second vehicle and a lateral acceleration of the first vehicle away from the second vehicle is smaller than a predetermined threshold.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims priority to European Patent Application Number21155970.3, filed Feb. 9, 2021, the disclosure of which is herebyincorporated by reference in its entirety herein.

BACKGROUND

Autonomous driving functionality is a feature of modern vehicles whichhas been attracting increasing interest. Autonomous drivingfunctionality may allow the driver of a host vehicle (i.e. the vehicleto be autonomously controlled) to hand over the control of bothacceleration and steering of the vehicle to an autonomous drivingsystem, which may be provided with a target velocity and headway time ormore detailed information of an intended route. The autonomous drivingsystem may then attempt to achieve the desired velocity throughacceleration and steer the vehicle so as to follow a chosen lane.

An autonomous driving system may be further adapted to reactappropriately to the actions of other road-users. For example, when thehost vehicle approaches a slower-moving vehicle ahead of it, theautonomous driving system may decide whether to overtake theslower-moving vehicle or to slow down and to keep a desired headwaydistance to the vehicle ahead. The autonomous driving system mayadditionally switch lanes to follow a desired route. More advancedversions of the system may even predict the behaviour of otherroad-users to determine appropriate actions and reactions. Accordingly,autonomous driving systems are generally configured to obtaininformation from equipment such as radars, cameras, inertial measurementunits etc., in order to collect data about the host vehicle and itsenvironment and generate a high-level environment model describing theroad and the traffic on it.

The autonomous driving system may then be further arranged to identifyone or more manoeuvres that the host vehicle may perform based on thegenerated high-level environment, to select a manoeuvre to be performed,and to determined how this manoeuvre may be executed (in other words, todetermine a trajectory for the host vehicle and appropriate controlsignals, such as for an acceleration and a steering angle of the hostvehicle, that are required to achieve the determined trajectory), and tocontrol the host vehicle to perform the determined manoeuvre. The twomain approaches to autonomous driving algorithms are rule-based, andstatistical models including those based on machine learning, costfunctions, etc.

SUMMARY

Example aspects herein generally relate to the field of autonomousdriving, in particular, to techniques for determining whether a plannedtrajectory for use in autonomous control of a vehicle is invalid. Thepresent inventor has devised, in accordance with a first aspect herein,a computer-implemented method of determining whether a plannedtrajectory of a first model vehicle over a model of a road along whichthe first model vehicle and a second model vehicle are traveling, foruse in autonomous control of a vehicle modeled by the first modelvehicle, is invalid, the model of the road comprising a plurality oflanes defined by a plurality of lane boundaries. The method comprisesobtaining the planned trajectory, the planned trajectory comprising arespective first vehicle state of the first model vehicle definedrelative to the model of the road for each of a plurality of timeinstants, each first vehicle state being defined by a respective lateralposition of the first model vehicle, a respective lateral velocity ofthe first model vehicle, and a respective lateral acceleration of thefirst model vehicle. The method further comprises obtaining a secondvehicle state of the second model vehicle defined relative to the modelof the road for each of the plurality of time instants, each secondvehicle state being defined by a respective lateral position of thesecond model vehicle in the model of the road. The method furthercomprises determining, for each of the plurality of time instants, arespective lateral range extending from the second model vehicle, usinga respective lateral position of the second model vehicle relative to acentre of a lane among the plurality of lanes in which the second modelvehicle is located. The method further comprises determining that theplanned trajectory is invalid in a case where, for the first vehiclestate and the second vehicle state for at least one time instant of theplurality of time instants, the following conditions of a first set ofconditions are satisfied: (i) the lateral position of the first modelvehicle is within the lateral range of the second model vehicle at thetime instant and within a lane boundary region extending along andcomprising a lane boundary of the plurality of lane boundaries; and (ii)a direction of the lateral velocity of the first model vehicle istowards the second model vehicle and a magnitude of the lateralacceleration of the first model vehicle away from the second modelvehicle is less than a predetermined lateral deceleration of the firstmodel vehicle.

The present inventor has further devised, in accordance with a secondaspect herein, a computer program comprising instructions, which, whenexecuted by a computer processor, cause the computer processor toperform the method according to the first aspect. The computer programmay be stored on a non-transitory computer-readable storage medium orcarried by a signal.

The present inventor has further devised, in accordance with a thirdaspect herein, an apparatus arranged to determine whether a plannedtrajectory of a first model vehicle over a model of a road along whichthe first model vehicle and a second model vehicle are traveling, foruse in autonomous control of a vehicle modeled by the first modelvehicle, is invalid, the model of the road comprising a plurality oflanes defined by a plurality of lane boundaries. The apparatus comprisesa planned trajectory obtaining module configured to obtain the plannedtrajectory, the planned trajectory comprising a respective first vehiclestate of the first model vehicle defined relative to the model of theroad for each of a plurality of time instants, each first vehicle statebeing defined by a respective lateral position of the first modelvehicle, a respective lateral velocity of the first model vehicle and arespective lateral acceleration of the first model vehicle. Theapparatus further comprises a second vehicle state obtaining moduleconfigured to obtain a second vehicle state of the second model vehicledefined relative to the model of the road for each of the plurality oftime instants, each second vehicle state being defined by a respectivelateral position of the second model vehicle in the model of the road.The apparatus further comprises a lateral range determining moduleconfigured to determine, for each of the plurality of time instants, arespective lateral range extending from the second model vehicle, usinga respective lateral position of the second model vehicle relative to acentre of a lane among the plurality of lanes in which the second modelvehicle is located. The apparatus further comprises a validitydetermining module configured to determine that the planned trajectoryis invalid in a case where, for the first vehicle state and the secondvehicle state for at least one time instant of the plurality of timeinstants, the following conditions of a first set of conditions aresatisfied: (i) the lateral position of the first model vehicle is withinthe lateral range of the second model vehicle at the time instant andwithin a lane boundary region extending along and comprising a laneboundary of the plurality of lane boundaries; and (ii) a direction ofthe lateral velocity of the first model vehicle is towards the secondmodel vehicle and a magnitude of the lateral acceleration of the firstmodel vehicle away from the second model vehicle is less than apredetermined lateral deceleration of the first model vehicle.

The present inventor has further devised, in accordance with a fourthaspect herein, a vehicle comprising an automatic driver system and anapparatus according to the first aspect, which is arranged to determinewhether a planned trajectory is invalid. The apparatus is furtherarranged to determine, in a case where the planned trajectory is notdetermined to be invalid, that the planned trajectory is a valid plannedtrajectory and to output the valid planned trajectory to the automaticdriver system, the automatic driver system being arranged toautonomously control the vehicle to drive along a road in accordancewith the valid planned trajectory.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the disclosure will now be explained in detail, by way ofnon-limiting example only, with reference to the accompanying figures,described below. Like reference numerals appearing in different ones ofthe figures can denote identical or functionally similar elements,unless indicated otherwise.

FIG. 1A is a schematic illustration of an apparatus arranged todetermine whether a planned trajectory of a first model vehicle, for usein autonomous control of a vehicle modeled by the first model vehicle,is invalid, according to an example embodiment herein.

FIG. 1B is a schematic illustration of a vehicle, according to theexample embodiment herein.

FIG. 2A illustrates an example of a model of a road defined in a lanecoordinate system.

FIG. 2B illustrates an example of a planned trajectory of the firstmodel vehicle over the model of a road of FIG. 2A.

FIG. 3 is a block diagram illustrating an example implementation of theapparatus of the example embodiment in programmable signal processinghardware.

FIG. 4 is a flow diagram illustrating a process by which the apparatusof the example embodiment determines a target lateral acceleration of ahost vehicle.

FIG. 5 is a plot illustrating a variation of a left range calculatedusing a lateral range function described herein.

FIG. 6A is a schematic illustration showing an example of the lateralrange determined by the lateral range determining module of theapparatus of FIG. 1 .

FIG. 6B is a schematic illustration showing an example of the lateralrange determined by the lateral range determining module of theapparatus 10 of FIG. 1 at a particular time instant when the secondmodel vehicle moves into the lane boundary region.

FIG. 6C is a schematic illustration showing a first example in which thelateral range determining module determines a left part and a right partof the lateral range of FIG. 6A.

FIG. 6D is a schematic illustration showing a second example in whichthe lateral range determining module determines a left part and a rightpart of the lateral range of FIG. 6A.

FIG. 7 is a schematic illustration showing an example of the brakingregion determined by the apparatus of FIG. 1 .

FIG. 8 is a schematic illustration showing an example of all regionsdefined by the process of FIG. 4 , in accordance with an exampleembodiment herein.

FIGS. 9A and 9B are schematic illustration showing an example of allregions defined by the process of FIG. 4 for each of a first cell O_1and a second cell O_n of a plurality of cells representing the secondmodel vehicle O.

DETAILED DESCRIPTION

To be considered roadworthy, vehicles incorporating autonomous drivingfunctionality are generally required to provide a high level of safety.While the safety's dependency on sensing equipment only can be provenwith respect to likelihood, the algorithms used by autonomous drivingsystems for behavioural control and trajectory planning can be provensafe using formal models such as, Responsibility-Sensitive Safety (RSS),for example. RSS is a formal model describing allowed behaviour toguarantee safety.

However, various difficulties can arise both in implementing autonomousdriving systems such that the determined behaviours and trajectories ofthe autonomously controlled vehicle are safe and resemble human-likebehaviour (i.e. such that the autonomous control of the vehiclecorresponds to the manual control performed by a safe human driver), andin formally proving the safety of autonomous driving systems, which maybe overcome in order to provide roadworthy autonomous driving.

By way of example, autonomous driving algorithms based on statisticalmodels can lack transparency compared to rule-based models. Rule-basedmodels allow prediction of what will happen in any given situation, anda decision regarding actions that are consequently to be taken, to belinked to specific rules. In contrast, a crash caused by decision madeby a statistical model (such as a machine learning model) may be harderto justify, and the causes may be more difficult or impossible todetermine. The present inventor has recognised that, when generalisingto an arbitrary number of vehicles in the host vehicle's environment,the behaviour in many conventional autonomous driving algorithms thatare based on cost functions may have to be analysed on a case-by casebasis with respect to the number of vehicles and all possibleconstellations of these vehicles, in order to determine safety. It isimportant that a trajectory generated by any of these algorithms can bevalidated and thus deemed safe before being used to control the hostvehicle.

As such, otherwise advantageous autonomous driving algorithms based onstatistical models such as machine learning or cost-functions withoptimizers may be hard to analyse to such degree that mathematicalguarantees of safety can be made.

Accordingly, rather than analysing an autonomous algorithm based onstatistical models directly, the present inventor has recognised thatsimpler interpretable models of safety can be developed which can thenbe applied to the trajectories generated by the autonomous drivingalgorithm and used to validate these trajectories after they have beengenerated.

By way of example, a trajectory generated by an autonomous algorithmbased on statistical models may be assessed using the rules of the RSSmodel, which define safe distances to be maintained between vehicles.However, while the RSS model may be sufficient to increase safety withrespect to emergency manoeuvres, as this model may prevent vehiclecollisions from a safe state, it does not define conditions for safebehaviour with respect to lanes of the road. As such, the simplestpolicies that comply with the rules of the RSS model may result in, forexample, scenarios in which a vehicle is allowed to get stuck betweenother vehicles between lanes, in a case where the vehicle has avoidedimmediate danger but is unable to return to a safe lateral distance.

Furthermore, the distances defined by the RSS model are based onexpecting emergency manoeuvres which, while safe, may not guaranteecomfortable, human-like driving.

A modified Responsibility-Sensitive Safety (MRSS) model is proposed inthe Master's Thesis of Oskar Larsson titled “The Oskillator, ArtificialForce Field Highway Chauffeur” Chalmers University of Technology,Gothenburg, Sweden 2019 (https://hdl.handle.net/20.500.12380/300733),the contents of which are incorporated herein in their entirety. In theMRSS model, a safe lateral distance is defined as a minimum lateralevasive distance, but not only to the other vehicles themselves, but toall lanes within a minimum lateral evasive distance of the othervehicle. This approach allows it to be ensured that collisions betweenvehicles are avoided and to avoid vehicles turning into a same lane andthus possible unsafe scenarios arising. As such, this approach takesinto consideration the required behaviour of a host vehicle with respectto lanes of road.

However, the present inventor has recognised that neither of thesesafety models take into consideration how a host vehicle may betterrespond when other road-users engage in unsafe driving that breaks therules defined by these safety models.

By way of example, unsafe driving may include, for example, cases whereanother road-user trailing a host vehicle is dangerously close to thehost vehicle, i.e. trails the host vehicle by a distance that is lessthan an emergency distance which the trailing road user may require toperform an emergency braking manoeuvre. Another example of unsafedriving may occur where another road-user moves into a lane in which thehost vehicle is driving at a dangerously close distance behind or infront of the host vehicle.

In such cases, a human driver may, for example, control their vehicle tostay in the same lane or to switch into another lane. Such manoeuvresmay be considered by a safe human driver to represent a best response toa dangerous scenario caused by the other road-user. However, for both ofthese manoeuvres, application of the rules of the RSS model or the MRSSmodel will result in corresponding trajectories generated by anautonomous driving algorithm being invalidated as the host vehicle may,according to the rules of these models, be dangerously close to theother road-user initially.

As such, the present inventor has recognised that the application of therules of existing safety models may result in trajectories generated byan autonomous driving algorithm being invalidated as dangerous, evenwhere such trajectories represent a best response (i.e. any safetyissues are unavoidable and do not immediately endanger the driver orother road-users) to a dangerous situation caused by the unsafe drivingof another road-user.

Furthermore, the present inventor has recognised that some existingsafety models, such as the MRSS model, do not discuss how to validate anactual trajectory generated by an autonomous driving algorithm using thedefined rules.

Example embodiments described in the following may address one or moreof the issues outlined above and will now be described in detail withreference to the accompanying drawings. Where technical features in thedrawings, detailed description or any claim are followed by referencesigns, the reference signs have been included for the sole purpose ofincreasing the intelligibility of the drawings, detailed description,and claims. Accordingly, neither the reference signs nor their absenceshould be interpreted to have any limiting effect on the scope of anyclaim elements.

FIG. 1A is a schematic illustration of an apparatus 10 arranged todetermine whether a planned trajectory of a first model vehicle, for usein autonomous control of a vehicle 1 modeled by the first model vehicle,is invalid, according to an example embodiment herein.

More particularly, the apparatus 10 is arranged to determine whether aplanned trajectory of the first model vehicle over a model of a road 20(shown in FIG. 2A) along which the first model vehicle and a secondmodel vehicle O (shown in FIG. 2A) are traveling, for use in autonomouscontrol of a vehicle 1 modeled by the first model vehicle, is invalid.The model of the road 20 includes a plurality of lanes 21A, 21B, 21Cdefined by a plurality of lane boundaries. By way of example, thevehicle 1 may, as in the present example embodiment, be considered as ahost vehicle (i.e. a vehicle to be autonomously controlled).

FIG. 2A illustrates an example of a model of a road 20 defined in a lanecoordinate system. The model of the road 20 is an example of a modeledroad along which the first model vehicle and the second model vehicle Omay travel.

In the example of FIG. 2A, the road 20 has three lanes 21A, 21B and 21Cdefined by a plurality of lane boundaries 22A, 22B, 22C, 22D (shown inFIG. 2B). The lanes of the road 20 may, as in the present example, havethe same width. One of the lanes 21A, 21B, 21C may, as in the presentexample, serve as a so-called “fast lane” and another of the lanes 21A,21B, 21C may serve as a so-called “slow lane”. In the present example,the leftmost lane 21A serves as the fast lane and the rightmost lane 21Cserves as the slow lane.

The exemplary model of the road 20 shown in FIG. 2A illustrates the road20 and the traffic thereon at a particular instant in time. In theexemplary model of the road 20, the first model vehicle is located at aposition 26 in the middle lane 21B and traveling in the directionindicated by arrow 27. The second model vehicle O (e.g. a vehicle ofanother road-user, that is a road-user other than the first modelvehicle) is traveling in the right-most lane 21C in the same directionas the first model vehicle.

The position of the first model vehicle and of the second model vehicleO in the model of the road 20 may, as in the present example, be definedwith respect to a centre of a bounding box of each vehicle. By way ofalternative, the position of the first model vehicle and the secondmodel vehicle O may be defined by in relation to any other predefinedreference point on the model vehicle such as, for example, apredetermined corner of the bounding box of the model vehicle, a centreof mass of the model vehicle, a centroid of the model vehicle, etc.

Although the model of the road 20 shown in FIG. 2A has three lanes, theroad on which the model of the road 20 is based may have one lane, twolanes or four or more lanes and a corresponding number of lanes may beincluded in the model of the road 20. By way of further alternative,while a single second model vehicle O is shown in the model of the road20 illustrated in FIG. 2A, any suitable number of model vehicles otherthan the first model vehicle may be included in a model of a road 20and, optionally, the number of additional model vehicles may depend onthe traffic on the road at a given time. By way of example, the numberof additional model vehicles may be determined from information fromequipment such as radars, cameras, inertial measurement units etc. thatcollect data about the vehicle 1 and its environment in order togenerate a high-level environment model describing the road and thetraffic on it, i.e. the model of the road 20.

In the example of FIG. 2A, the model of the road 20 is defined in a lanecoordinate system. The lane coordinate system may be a two-dimensionalcurvilinear coordinate system adapted to reflect the road on which themodel of the road 20 is to be based. In particular, a curvilinearcoordinate system constituting the lane coordinate system has two axes,namely a longitudinal axis or x-axis (indicated by reference sign x inFIG. 2A) which extends in a longitudinal direction along the road and alateral axis or y-axis (indicated by reference sign y in FIG. 2A) whichextends across the road. The x-axis is always parallel to the lanes ofthe road and the y-axis is orthogonal to the x-axis at every value of x.By way of alternative, the lane coordinate system and thus the model ofthe road 20 may be defined by any other suitable means, such as by usinga Cartesian coordinate system or any other suitable coordinate system.

More generally, the lane coordinate system and the model of the road 20may be defined in any suitable way such that the apparatus 10 isprovided with information on the position of the first model vehicle,the number and width of lanes 21A, 21B, 21C, the position and velocityof the second model vehicle O and any additional model vehicles on theroad, and optionally also the curvature of the road 20.

In the example lane coordinate system shown in FIG. 2A, the x-axis ofthe lane coordinate system is increasing in the direction of forwardtravel of the first model vehicle and the y-axis of the lane coordinatesystem is increasing in the direction of the leftmost lane 21A of themodel of the road 20. However, the lane coordinate system may beorientated in any other suitable way. By way of example, the x-axis ofthe lane coordinate system may be increasing in a direction opposite tothe direction of forward travel of the first model vehicle and/or they-axis may be increasing in a direction of the rightmost lane of themodel of road 20.

Furthermore, the lane coordinate system may, as in the example of FIG.2A, be defined such that x=0 denotes the position of the first modelvehicle in the x-axis and y=0 denotes the centre of a lane of the road20. In particular, the lane coordinate system may, as in the example ofFIG. 2A, be defined such that y=0 denotes the centre of the centre lane21B. However, the lane coordinate system may be defined in any othersuitable manner, e.g. y=0 may be selected denote the centre of any laneamong the plurality of lanes of the model of road 20.

As shown in FIG. 1A, the apparatus 10 includes a planned trajectoryobtaining module 11, a second vehicle state obtaining module 12, alateral range determining module 13, and a validity determining module14.

The planned trajectory obtaining module 11 is configured to obtain aplanned trajectory, the planned trajectory comprising a respective firstvehicle state of the first model vehicle defined relative to the modelof the road for each of a plurality of time instants, each first vehiclestate being defined by a respective lateral position of the first modelvehicle, a respective lateral velocity of the first model vehicle and arespective lateral acceleration of the first model vehicle.

In particular, it is assumed that sufficient information and data aboutthe vehicle 1 and its environment may be obtained from equipment such asradars, cameras, inertial measurement units etc., so that the model ofthe road 20 generated therefrom may describe the estimated future stateof the environment of the vehicle (e.g. the road and the trafficthereon). That is, while the example of the model of the road 20 shownin FIG. 2A illustrates the road and the traffic thereon, i.e. theestimated state of the environment, at a particular instant in time, themodel of the road 20 may, as in the present example embodiment, furtherdescribe the estimated state of the environment for a plurality offuture time instants. For example, the model of the road 20 may describethe estimated state of the environment at different time instants duringa set period of time in the future starting from, for example, a presenttime instant or a next future time instant.

By way of more specific example, the set period may be between 0.1 and 5seconds, and the model of the road 20 may include an estimated state ofthe environment for each of a plurality of time instants in that setperiod. The plurality of time instants may correspond to a plurality oftime steps with a set time interval between each pair of successive timeinstants. For example, the model of the road 20 may include a pluralityof estimated states of the environment at 0.25-second intervals over aperiod of 5 seconds. The intervals may be short enough for the use oflinear interpolation or an assumption of constant velocity oracceleration to yield a sufficiently accurate representation of thevehicle state at that time.

FIG. 2B illustrates an example of a planned trajectory 24 of the firstmodel vehicle over the model of a road 20 of FIG. 2A. In particular,FIG. 2B illustrates a section of the model of the road 20 over which theroad is approximately linear.

In the model of the road 20, the y-axis may, as in the present exampleshown in FIG. 2B, be scaled to the lane width such that each incrementor decrement of 1 in the y-axis represents the width of one lane, suchthat y=1 denotes the centre of the leftmost lane 21A and y=−1 denotesthe centre of the rightmost lane 21C and y={−1.5, −0.5, 0.5, 1.5} denotethe lane boundaries 22A, 22B, 22C, 22D of lanes 21A, 21B and 21C.Alternatively, the y-axis may be scaled in any other suitable manner,e.g. such that each increment or decrement of 1 in the y-axis representshalf the width of one lane so that both the lane centres and so laneboundaries have integer values or the y-axis may not be scaled.

Additionally, or alternatively, the model of the road 20 may, as in thepresent example shown in FIG. 2B, include a plurality of lane boundaryregions 23A, 23B, 23C, 23D. Each lane boundary region 23A, 23B, 23C, 23Dextends along and comprising a respective lane boundary 22A, 22B, 22C,22D of the plurality of lane boundaries.

Each lane boundary region may, as in the present example, be definedusing a lateral offset Δy_(bias) from the centre of the correspondinglane. The value of the lateral offset Δy_(bias) may be selected so as torepresent an acceptable deviation from the lane centre (bias leeway)that a vehicle may have while still being considered to remain fully(safely) within the lane. In particular, in order to ensure safety, thefirst model vehicle may stay near the centre of a lane in which istraveling unless the first model vehicle is switching lanes and thelateral offset Δy_(bias) may be selected so as to represent the maximallateral deviation from a centre of the lane the first model vehicle mayappropriately have when not switching lanes. Accordingly, the laneboundary region may correspond to the part of each lane 21A, 21B, 21C,on either side of a lane boundary 22A, 22B, 22C, 22D which is more thanthe lateral offset Δy_(bias) from the centre of that lane 21A, 21B, 21C.

By way of more specific example, the lane boundary regions R_(l) may, asin the present example, be formally defined as follows:R _(l)={(x,y)∈R ² s.t. {tilde over (y)}<−Δy _(bias) or Δy _(bias)<{tilde over (y)}},  (1)

where {tilde over (y)}∈[−0.5, 0.5) and {tilde over (y)}=((y+0.5)mod1)−0.5

The planned trajectory 24 includes a respective first vehicle state ofthe first model vehicle defined relative to the model of the road 20 foreach of a plurality of time instants. By way of example, in the exampleshown in FIG. 2B, the planned trajectory includes nine first vehiclestates defined by a respective lateral position 25_1 to 25_9 of thefirst model vehicle. Although not shown in FIG. 2B, each of the firstvehicle states is further defined by a respective lateral velocity ofthe first model vehicle and a respective lateral acceleration of thefirst model vehicle.

As such, in the example shown in FIG. 2B, the planned trajectory 24defines a manoeuvre by which the first model vehicle moves from lane 21Binto lane 21A in nine steps by defining the state of the first modelvehicle in terms of lateral positions, lateral velocity and lateralacceleration (that is, the first vehicle state) at each of ninesuccessive time instants while executing this manoeuvre. In the presentexample, the plurality of time instants includes nine time instants.However, as discussed above, any suitable number of time instants may beconsidered.

Optionally, the respective first vehicle state of each of the pluralityof time instants may further include any additional information definingthe state of the first model vehicle. By way of non-limiting example,the first vehicle state may additionally include one or more of alongitudinal position of the first model vehicle, a longitudinalvelocity of the first model vehicle, a longitudinal acceleration of thefirst model vehicle, a lateral extent or width of the first modelvehicle and a longitudinal extent or length of the first model vehicle.

By way of example, the first vehicle state for each of the plurality oftime points may, as in the present example embodiment, be defined by thefollowing information of the first model vehicle:

-   -   l—longitudinal extent (length)    -   w—lateral extent (width)    -   y—lateral position    -   v_(x)—longitudinal velocity    -   v_(y)—lateral velocity    -   a_(x)—longitudinal acceleration    -   a_(y)—lateral acceleration

More generally, the first model vehicle and any additional modelvehicles may, as in the present example, be represented as an objecthaving dynamic properties as described above defined in the lanecoordinate system. As will be discussed in more detail below, the firstmodel vehicle and any additional model vehicles may alternatively berepresented as one or more cells of a grid having dynamic propertiesdefined in the lane coordinate system.

Referring again to FIG. 1A, the second vehicle state obtaining module 12is configured to obtain a second vehicle state of the second modelvehicle O defined relative to the model of the road 20 for each of theplurality of time instants, each second vehicle state being defined by arespective lateral position of the second model vehicle O in the modelof the road 20.

By way of example, similar to the first vehicle state, the secondvehicle state for each of the plurality of time instants may, as in thepresent example, be represented as an object having dynamic propertiesdefined in the lane coordinate system. As will be discussed in moredetail below, the first model vehicle and any additional model vehiclesmay alternatively be represented as one or more cells of a grid havingdynamic properties defined in the lane coordinate system.

By way of more specific example, the second model vehicle O may, as inthe present example embodiment, be defined by a coordinate identifying alocation of the second model vehicle O in a lane coordinate system ofthe model of the road 20, a length of the second model vehicle along alongitudinal axis of the lane coordinate system, and a width of thesecond model vehicle along a lateral axis of the lane coordinate system.By way of alternative, the second model vehicle O may be defined by oneor more cells of a grid defined in the lane coordinate system, as willbe discussed in more detail below.

By way of further example, the respective second vehicle state of eachof the plurality of time instants may optionally further include anyadditional information defining the state of the second model vehicle O.By way of non-limiting example, the second vehicle state mayadditionally include one or more of a longitudinal position of thesecond model vehicle O, a longitudinal velocity of the second modelvehicle O, a lateral velocity of the second model vehicle O, alongitudinal acceleration of the second model vehicle O, a lateralacceleration of the second model vehicle O, a longitudinal extent orlength of the first model vehicle, and a lateral extent or width of thesecond model vehicle O.

By way of example, the second vehicle state for each of the plurality oftime points may, as in the present example embodiment, be defined by thefollowing information of the second model vehicle O (where the subscripti denotes that the second model vehicle O may be the i^(th) modelvehicle among one or more model vehicles defined in the model of theroad 20 in addition to the first model vehicle):

-   -   l_(i)—longitudinal extent (length)    -   w_(i)—lateral extent (width)    -   x_(i)—longitudinal position    -   y_(i)—lateral position    -   v_(x,i)—longitudinal velocity    -   v_(y,i)—lateral velocity    -   a_(x,i)—longitudinal acceleration    -   a_(y,i)—lateral acceleration

The lateral range determining module 13 is configured to determine, foreach of the plurality of time instants, a respective lateral rangeextending from the second model vehicle O, using a respective lateralposition of the second model vehicle O relative to a centre of a lane21C among the plurality of lanes in which the second model vehicle O islocated.

The validity determining module 14 is configured to determine that theplanned trajectory is invalid in a case where, for the first vehiclestate and the second vehicle state for at least one time instant of theplurality of time instants, the following conditions of a first set ofconditions are satisfied:

-   -   (i). the lateral position of the first model vehicle is within        the lateral range of the second model vehicle O at the time        instant and within a lane boundary region 23A, 23B, 23C, 23D        extending along and comprising a lane boundary 22A, 22B, 22C,        22D of the plurality of lane boundaries; and    -   (ii). a direction of the lateral velocity of the first model        vehicle is towards the second model vehicle O and a magnitude of        the lateral acceleration of the first model vehicle away from        the second model vehicle O is less than a predetermined lateral        deceleration of the first model vehicle.

FIG. 1B is a schematic illustration of a vehicle 1, according to anexample embodiment herein. The vehicle 1 may, as in the present exampleembodiment, be considered as a host vehicle (i.e. a vehicle to beautonomously controlled) and serves as an example of a vehicle that maybe modeled by the first model vehicle.

The vehicle 1 includes an automatic driver system 15 and the apparatus10, which is arranged to determine whether a planned trajectory isinvalid. In the example embodiment of FIG. 1B, the apparatus is furtherarranged to determine, in a case where the planned trajectory is notdetermined to be invalid, that the planned trajectory is a valid plannedtrajectory and to output the valid planned trajectory to the automaticdriver system 15.

The automatic driver system 15 is arranged to autonomously control thevehicle 1 to drive along a road in accordance with the valid plannedtrajectory. By way of example, the automatic driver system 15 may bearranged to generate control signals for controlling steering and/oracceleration of the vehicle 1 to cause vehicle 1 to perform a manoeuvrein accordance with the valid planned trajectory or the control thevehicle 1 by any other suitable means.

The combination of the automatic driver system 15 and the apparatus 10may be referred to as an autonomous driving system, i.e. one capable ofperforming behaviour and trajectory planning and subsequent control ofthe host vehicle.

In the example embodiment shown in FIG. 1B, the apparatus 10 and theautomatic driver system 15 are illustrated as separate devices. Thefunctionalities of the apparatus 10 and the automatic driver system 15may alternatively be provided by an appropriately configured singledevice, e.g. an appropriately programmed computer processor.

Alternatively, the apparatus 10 may be used to determine whethertrajectories are invalid as part of simulation of autonomouslycontrolled vehicles or as part of testing and analysis of autonomousdriving algorithms, such as autonomous driving algorithms based onstatistical models, for example. For example, when training ArtificialIntelligence or machine learning models, it is often useful to have aterminating condition, as in reinforcement learning, for example, wherethe agent learning has either succeeded or failed. As such, validplanned trajectories that are suitable for use in autonomous control ofthe vehicle 1 modeled by the first model vehicle may not necessarily beused to control the vehicle 1.

As will be apparent from the present disclosure, in order to for thevalidity determining module 14 of the apparatus 10 to determine that theplanned trajectory is invalid, autonomously controlling the vehicle 1 inaccordance with the planned trajectory may, for at least one timeinstant, bring the first model vehicle within a certain lateral distanceof the second model vehicle O, i.e. within the lateral range of thesecond model vehicle. As such, the apparatus 10 of FIG. 1A may allow aplanned trajectory to be determined as invalid if a safe lateraldistance to the second model vehicle is not maintained.

However, in order for the validity determining module 14 to determinethat the planned trajectory is invalid, at the at least one time instantat which the lateral position of the first model vehicle is in withinthe first lateral range, the lateral position of the first model vehiclemay also be within a lane boundary region. As such, in cases where alateral position of the first model vehicle at a particular time instantis within a region of the lane 21C, in which the second model vehicle Ois driving, directly ahead of the second model vehicle O or within aregion of the lane 21C, in which the second model vehicle O is drivingdirectly behind of the second model vehicle O (that is, in a case wherea lateral position of the first model vehicle at a particular timeinstant is within a certain distance of the centre of that lane 21C inwhich the second model vehicle is driving), the condition (i) above willnot be satisfied.

Accordingly, in cases where the second model vehicle O representsanother road-user that trails the first model vehicle at a dangerouslyclose distance or that moves into a lane in which the first modelvehicle is driving at a dangerously close distance behind the firstmodel vehicle, a planned trajectory that may cause the vehicle 1 to beautonomously controlled to remain in the lane in which it is driving maynot be determined as invalid, even though the lateral position of thefirst model vehicle at most, if not all, of the plurality of timeinstants for such a planned trajectory may be within the determinedlateral range of the second model vehicle. In particular, for a plannedtrajectory that does not cause a switching of lanes, the first modelvehicle normally does not enter the lane boundary regions of the lane inwhich it is driving but will remain near the centre of the lane suchthat the second part of condition (i) will not be satisfied.

Therefore, the apparatus 10 may avoid that planned trajectories thatrepresent a best response (e.g. remaining in a same lane) to the unsafedriving of another road user are determined invalid.

Furthermore, in order to for the validity determining module 14 todetermine that the planned trajectory is invalid, at the at least onetime instant at which the first model vehicle is within the lateralrange of the second model vehicle O and within a lane boundary region23A, 23B, 23C, 23D, the direction of the lateral velocity of the firstmodel vehicle may be towards the second model vehicle O and a magnitudeof the lateral acceleration of the first model vehicle away from thesecond model vehicle O may be less than a predetermined lateraldeceleration of the first model vehicle.

In cases where the second model vehicle represents another road-userthat trails the first model vehicle at a dangerously close distance orthat moves into a lane in which the first model vehicle is driving at adangerously close distance behind the first model vehicle, a plannedtrajectory that may cause the vehicle 1 to be autonomously controlled toswitch to another lane may result in the direction of the lateralvelocity of the first model vehicle being away from the second modelvehicle O and/or the lateral acceleration of the first model vehicleaway from the second model vehicle O being greater than or equal to apredetermined lateral deceleration of the first model vehicle. Inparticular, in such cases, in which the second model vehicle O isdriving in a same lane as the first model vehicle, moving to anotherlane by the first model vehicle result in an increase in the lateraldistance between the first model vehicle and the second model vehicle O,which in turn necessities the first model vehicle laterally acceleratingaway from the second model vehicle O and/or the lateral velocity of thefirst model vehicle being away from the second model vehicle O.

Therefore, in such cases where the second model vehicle O representsanother road-user that trails the first model vehicle at a dangerouslyclose distance or that moves into a lane in which the first modelvehicle is driving at a dangerously close distance behind the firstmodel vehicle, a planned trajectory that may cause the vehicle 1 to beautonomously controlled to switch into a different lane may not bedetermined as invalid, as condition (ii) will not be satisfied.

Therefore, the apparatus 10 may further avoid that other plannedtrajectories that represent a best response (e.g. switching to anotherlane) to the unsafe driving of another road user are determined invalid.

However, the apparatus 10 may still determine as invalid plannedtrajectories that may, for example, cause the vehicle 1 to beautonomously controlled to move into a same lane as the second modelvehicle O at a dangerously close distance or otherwise move to adangerously close lateral distance to the second model vehicle O (i.e.planned trajectories that cause unsafe driving on behalf of the firstmodel vehicle) as in these cases, the first model vehicle may have topass through a lane boundary region, the lateral velocity of the firstmodel vehicle may need to be towards the second model vehicle O and thefirst model vehicle may either accelerate towards the second modelvehicle O or have minimal acceleration away from the second modelvehicle O.

Therefore, the apparatus 10 may ensure that planned trajectories thatmay cause the vehicle 1 to be autonomously controlled to drive unsafelymay be invalidated.

Furthermore, by obtaining a first vehicle state and a second vehiclestate for each of the plurality of time instants and determining whetherthe planned trajectory is invalid when conditions (i) and (ii) aresatisfied for even one time instant of the plurality of time instants,the apparatus 10 may allow the safety of the entire planned trajectoryto be analysed.

As such, the apparatus 10 may address one or more of the issues outlinedabove in relation to conventional approaches to trajectory validation.

FIG. 3 is a schematic illustration of programmable signal processingapparatus 300, which may be configured to implement the functionality ofthe apparatus 10. The signal processing apparatus 300 includes aninterface module 310 for receiving information and data about thevehicle 1 and its environment. The signal processing apparatus 300further includes a processor (CPU) 320 for controlling the apparatus 10,a working memory 330 (e.g. a random-access memory) and an instructionstore 340 storing a computer program comprising computer-readableinstructions which, when executed by the processor 320, cause theprocessor 320 to perform the processing operations of the apparatus 10.The instruction store 340 may include a ROM (e.g. in the form of anelectrically erasable programmable read-only memory (EEPROM) or flashmemory) which is pre-loaded with the computer-readable instructions.Alternatively, the instruction store 340 may include a RAM or similartype of memory, and the computer-readable instructions can be inputthereto from a computer program product, such as a computer-readablestorage medium 350 such as a CD-ROM, etc. or a computer-readable signal360 carrying the computer-readable instructions.

In the present example embodiment, the combination 370 of the hardwarecomponents shown in FIG. 3 , comprising the processor 320, the workingmemory 330 and the instruction store 340, is configured to implement thefunctionality of each of the component modules of the apparatus 10 shownin FIG. 1A.

FIG. 4 is a flow diagram illustrating a process by which the apparatus10 of FIG. 1A determines whether a planned trajectory of a first modelvehicle over a model of a road 20 along which the first model vehicleand a second model vehicle O are traveling, for use in autonomouscontrol of a vehicle 1 modeled by the first model vehicle, is invalid.The model of the road 20 includes a plurality of lanes defined by aplurality of lane boundaries.

In process step S41 of FIG. 4 , the planned trajectory obtaining module11 obtains the planned trajectory. The planned trajectory comprising arespective first vehicle state of the first model vehicle definedrelative to the model of the road 20 for each of a plurality of timeinstants, each first vehicle state being defined by a respective lateralposition of the first model vehicle, a respective lateral velocity ofthe first model vehicle and a respective lateral acceleration of thefirst model vehicle.

The planned trajectory obtaining module 11 may be configured to obtainthe planned trajectory in any suitable form.

For example, the apparatus 10 may, as in the present example embodiment,be configured to store the model of the road 20. The planned trajectoryobtaining module 11 may, as in the present example embodiment, beconfigured to receive a generated model of the road 20 including anestimated state of the environment of the vehicle at each of theplurality of time instants by any suitable means. By way of alternative,in some example embodiments, the planned trajectory obtaining module 11may be configured to receive information from equipment such as radars,cameras, inertial measurement units etc., that collect data about thevehicle 1 and its environment. The information may be in the form or rawor processed data. In such example embodiments, the planned trajectoryobtaining module 11 may be configured to generate the model of the road20 including an estimated state of the environment of the vehicle ateach of the plurality of time instants using the received information.

In such example embodiments, in which the apparatus 10 stores the modelof the road 20, the planned trajectory obtaining module 11 may, as inthe present example embodiment, be configured to obtain the plannedtrajectory by receiving information describing the planned trajectory inany suitable form from any entity capable of generating plannedtrajectories (e.g. an apparatus implementing an autonomous drivingalgorithm based on statistical models) and determining the respectivefirst vehicle state of the first model vehicle for each of a pluralityof time instants using the received information describing the plannedtrajectory and the stored model of the road 20.

By way of alternative, the planned trajectory obtaining module 11 may beconfigured to obtain the planned trajectory by receiving the respectivefirst vehicle state of the first model vehicle for each of a pluralityof time instants, e.g. in the form of an ordered plurality of firstvehicle states, from any suitable entity that may generate the firstvehicle states. For example, an apparatus implementing an autonomousdriving algorithm based on statistical models may, further to generatingtrajectories, may determine the first vehicle states corresponding to atrajectory and provide the first vehicle states to the plannedtrajectory obtaining module as the planned trajectory. In a simple form,the planned trajectory obtaining module 11 may, for example, beconfigured to obtain, as the respective first vehicle state of the firstmodel vehicle defined relative to the model of the road 20 for each of aplurality of time instants, a set of values for each of the plurality oftime instants.

In such example embodiments, the apparatus 10 may also store the modelof the road 20 or may be provided with only the information needed toperform the process of FIG. 4 , e.g. the positions of the centres of thelanes 21A, 21B, 21C of the road 20, the width of the lanes 21A, 21B, 21Cor the positions of the lane boundaries 22A, 22B, 22C, 22D, and thewidth of the lane boundary regions 23A, 23B, 23C, 23D or the width ofthe lateral offset Δy_(bias).

By way of further example, the planned trajectory obtaining module 11may be configured to obtain the planned trajectory by any suitable meansknown to those versed in the art. For example, the planned trajectoryobtaining module 11 may receive the planned trajectory via a directcommunication link (which may be provided by any suitable wired orwireless connection, e.g. a Universal Serial Bus (USB) or a Bluetooth™connection), or an indirect communication link (which may be provided bya network comprising a Local Area Network (LAN), a Wide Area Network(WAN) and/or the Internet). Furthermore, the planned trajectory may beobtained by the planned trajectory obtaining module 11 acquiring (e.g.by reading from a storage medium such as a CD or hard disk, or receivingvia a network such as the Internet) a planned trajectory that has beenprepared in advance.

In process step S42 of FIG. 4 , the second vehicle state obtainingmodule 12 obtains a second vehicle state of the second model vehicle Odefined relative to the model of the road 20 for each of the pluralityof time instants, each second vehicle state being defined by arespective lateral position of the second model vehicle O in the modelof the road 20.

The second vehicle state obtaining module 12 may be configured toreceive the second vehicle states for each of the plurality of timeinstants in any of the forms and by any of the means discussed above inrelation to process step S41 of the FIG. 4 .

In process step S43 of FIG. 4 , the lateral range determining module 13determines, for each of the plurality of time instants, a respectivelateral range 40 (shown in FIG. 6A) extending from the second modelvehicle O, using a respective lateral position of the second modelvehicle O relative to a centre of a lane 21C among the plurality oflanes in which the second model vehicle O is located.

The respective lateral range 40 determined for each of the plurality oftime instants may correspond to a safe lateral distance such as, forexample, a distance required to perform a lateral emergency manoeuvre ofreducing lateral velocity until the vehicle 1 is being driven in astraight line. As such, the lateral range 40 may be considered to definean extent on either side of the second model vehicle in which thepresence of the second model vehicle may be expected to affect theautonomous control of the vehicle 1, e.g. by placing some limitation ofits lateral movement, velocity or acceleration, in order to ensure safedriving of the autonomously controlled vehicle 1.

By way of example, the lateral range determining module 13 may, as inthe present example embodiment, determine the respective lateral range40 for each of the plurality of time instants using the respectivelateral position of the second model vehicle O relative to a centre ofthe lane 21C by evaluating, for each of the plurality of time instants,one or more functions that map a set of one or more input parameters orvariables, including the respective lateral position of the second modelvehicle O relative to a centre of the lane 21C, to a single output valueof the respective lateral range.

By way of alternative, in some example embodiments the lateral rangedetermining module 13 may determine the respective lateral range 40 foreach of the plurality of time instants by setting the lateral range 40as a predetermined distance extending in a first lateral direction andin a second lateral direction from the lateral position of the secondmodel vehicle O. That is, the respective lateral range 40 for each ofthe plurality of time instants may extend on either side of the secondmodel vehicle in the y-axis.

In such example embodiments, the lateral range determining module 13may, for example, use a respective lateral position of the second modelvehicle O relative to a centre of a lane 21C among the plurality oflanes in which the second model vehicle O is located to determine therespective lateral range 40 for each of the plurality of time instantsin that the predetermined distance set for each of the plurality of timeinstants is selected from a plurality of predetermined distances basedon the respective lateral position of the second model vehicle Orelative to a centre of a lane 21C among the plurality of lanes in whichthe second model vehicle O is located. For example, a largerpredetermined distance may be selected where the distance between thelateral position of the second model vehicle O and the centre of thelane 21C in which it is driving is relatively large (e.g. when thesecond model vehicle O is switching lanes). Alternatively, thepredetermined distance may have a fixed or constant value for each ofthe plurality of time instants and the respective lateral position ofthe second model vehicle O relative to a centre of a lane 21C among theplurality of lanes in which the second model vehicle O is located may beused only to determine from a lateral position from which the respectivelateral ranges 40 may extend.

In general, by using the respective lateral position of the second modelvehicle O relative to a centre of a lane 21C among the plurality oflanes in which the second model vehicle O is located to determine therespective lateral range 40 for each of the plurality of time instantssuch that the respective lateral range 40 increases with an increasingdistance between the lateral position of the second model vehicle O andthe centre of the lane 21C in which it is driving, the respectivelateral ranges 40 may, for example, be defined to reach past the nextlane of the second model vehicle O when it is performing a lane switchsuch that the first model vehicle is prohibited from performing asimultaneous lane switch into the same lane.

Additionally or alternatively, in example embodiments such as thepresent example embodiment, in which the lateral range determiningmodule 13 determines the respective lateral range 40 for each of theplurality of time instants by evaluating one or more functions, the oneor more input parameters or variables of the one or more functions mayinclude any suitable parameter(s) included in the second vehicle state.

By way of example, in example embodiments such as the present exampleembodiment, in which the second vehicle state for each of the pluralityof time instants is further defined by a respective lateral velocity ofthe second model vehicle O, the lateral range determining module 13 maybe further configured to determine the respective lateral range 40 foreach of the plurality of time instants using the respective lateralvelocity of the second model vehicle. By way of example, the lateralrange 40 determined for a particular time instant may be determined suchthat the lateral range 40 increases with increasing lateral velocity ofthe second model vehicle O.

This may help to ensure that, in a case where the second model vehicle Ois moving at a relatively high lateral velocity and, as such, mayapproach the first model vehicle relatively quickly, the determinedlateral range 40 used to determine whether the planned trajectory of thefirst model vehicle is valid is wider, and thus more plannedtrajectories may potentially be invalidated relative to the case wherethe second model vehicle O is moving at a relatively low lateralvelocity. As such, it may be better ensured that any planned trajectorydetermined to be a valid planned trajectory allows the first modelvehicle sufficient time and lateral distance to react where the secondmodel vehicle O is moving at a relatively high lateral velocity.

By way of more detailed example, the lateral range determining module 13may, as in the present example embodiment, determine the respectivelateral range 40 for each of the plurality of time instants by firstlydefining the following functions and sets:

$\begin{matrix}{{{clip}\left( {x,a,b} \right)} = {\min\left( {{\max\left( {a,x} \right)},b} \right)}} & (2)\end{matrix}$ $\begin{matrix}{{{interp}\left( {\left\lbrack {x_{1},{x_{2}\ldots x_{n}}} \right\rbrack,\left\lbrack {y_{1},{y_{2}\ldots y_{n}}} \right\rbrack,x} \right)} = \left\{ \begin{matrix}{y_{1},} & {x \leq x_{1}} \\{{y_{k} + {a\left( {y_{k + 1} - y_{k}} \right)}},} & {x_{k} \leq x \leq x_{k + 1}} \\{a = \frac{x - x_{k}}{x_{k + 1} - x_{k}}} & \\{y_{n},} & {x \geq x_{n}}\end{matrix} \right.} & (3)\end{matrix}$ $\begin{matrix}{{ys} = \left\lbrack {{- 0.5},{{- \Delta}y_{bias}},{\Delta y_{bias}},0.5} \right\rbrack} & (4)\end{matrix}$ $\begin{matrix}{{{rs} = \left\lbrack {{1.5 - {\Delta y_{bias}}},1,{1 - {\Delta y_{bias}}},{1.5 - {\Delta y_{bias}}}} \right\rbrack},} & (5)\end{matrix}$

and defining the following functions for use in determining a left partand a right part of the lateral range:

$\begin{matrix}{{\left. {{{\Delta{y_{base}(y)}} = {{interp}\left( {{ys},{rs},\overset{\sim}{y}} \right)}},{{{where}\overset{\sim}{y}} \in \left\lbrack {{- 0.5},0.5} \right.}} \right){and}\overset{\sim}{y}} = {\left( {y + {0.5{mod}1}} \right) - 0.5}} & (6)\end{matrix}$ $\begin{matrix}{{\Delta{y_{v,{range}}\left( {y,v} \right)}} = {{{interp}\left( {\left\lbrack {0,{\Delta y_{bias}},0.5} \right\rbrack,\left\lbrack {0,{1 - {\Delta y_{bias}}},0} \right\rbrack,\overset{\sim}{y}} \right)}{clip}\left( {\frac{v - v_{\mu}}{v_{\min,{switch}} - v_{\mu}},0,1} \right)}} & (7)\end{matrix}$ $\begin{matrix}{{\Delta{y_{range}\left( {y,v} \right)}} = {{\Delta{y_{base}(y)}} + {\Delta{{y_{v,{range}}\left( {y,v} \right)}.}}}} & (8)\end{matrix}$

In particular, using function (8) above, the left part of the lateralrange may be determined as Δy_(range)(y_(i), v_(y,i)), and the rightpart of the lateral range may be determined by anti-symmetry asΔy_(range)(−y_(i), −v_(y,i)).

In equation (7) above, v_(μ) is a threshold velocity (e.g. the peaklateral velocity to be used for biasing while driving within a samelane) below which the lateral range does not increase in order to avoidan increase of the lateral range being caused by small oscillations ofthe second model vehicle O and v_(min,switch) is a minimum lateralvelocity to be used during lane switching or that is indicative of laneswitching. By defining the functions for determining the left and rightparts of the lateral range 40 separately, it can be ensured that theextent of the lateral range 40 is only increased on the side of the lanein the direction of the velocity.

FIG. 5 is a plot illustrating a variation of a left range with positionwithin a lane, which has been calculated for an object component using alateral range function described herein so as to ensure that thecomponent is constant outside of the bias region whenever the vehicle isin the bias region and has a low lateral velocity. The range withlateral velocity v≤v_(μ) is shown by the solid line in FIG. 5 , whilethe range with lateral velocity v≥v_(min,switch) is shown by the dottedline in FIG. 5 . In between, it is given by linear interpolation betweenthe two. As illustrated in FIG. 5 , the left range decreases when movingleft from the center and increases when moving right. When the velocityto the left is higher, it will instead have an increased range movingaway from the lane center to the left.

In sets (4) and (5) and functions (6) to (8) above, it is assumed thatthe y-axis is scaled to the lane width such that each increment ordecrement of 1 in the y-axis represents the width of one lane, as in thepresent example embodiment, such that the value of 0.5 may represent thehalf the width of a lane of the road 20 (i.e. a distance between acentre of a lane and a boundary thereof). Alternatively, in exampleembodiments in which the y-axis is not so scaled, the value of 0.5 insets (4) and (5) and functions (6) to (8) may be replaced with anysuitable value corresponding to half of the width of a lane of the road20 and other values (e.g. 1.5, 1, etc.) may be scaled accordingly.

FIG. 6A is a schematic illustration showing an example of the lateralrange 40 determined by the lateral range determining module 13 of theapparatus 10 of FIG. 1 . The lateral range 40 may represent a respectivelateral range defined for a particular time instant among the pluralityof time instants.

The lateral range 40 shown in FIG. 6A may, as in the present exampleembodiment, be determined using the functions (6) to (8) above. By wayof alternative, the lateral range 40 may be determined by any suitablemeans as discussed above.

In the example shown in FIG. 6A, the lateral range 40 serves to define aregion 50 extending around the second model vehicle O, which regionextends not only laterally, along the y-axis but also longitudinally,along the x-axis. The longitudinal length of the region 50 may, forexample, be defined by the information obtained by the second vehiclestate obtaining module 12.

The second model vehicle state obtaining module 12 may be configured toconsider only additional model vehicles that are within a predeterminedlongitudinal distance of the first model vehicle. As such, the secondvehicle state may only be obtained for a second model vehicle which iswithin such a predetermined longitudinal distance of the first modelvehicle.

The apparatus 10 may, as in the present example embodiment, be furtherarranged to determine a longitudinal range extending from the secondmodel vehicle O in a first longitudinal direction and in a secondlongitudinal direction opposite to the first longitudinal direction(i.e. on either side of the second model vehicle O in the x-axis) as thelongitudinal length of the region 50. In such example embodiments, thelateral range determining module 13 may be further arranged to determinethe longitudinal range, or the apparatus 10 may include an additionalmodule which is arranged to determine a longitudinal range.

By way of an example, the determined longitudinal range may have a fixedvalue. The fixed value may, for example, correspond to a maximumlongitudinal safe distance defined as a distance required for thevehicle 1 to perform a longitudinal emergency manoeuvre such as brakingto stop in time to avoid a collision with another vehicle in a scenariowhere the vehicle 1 is traveling at a maximum permitted speed forvehicle 1 on public roads (e.g. a speed limit on a motorway) and theother vehicle is assumed to come to a stop instantaneously (wheninvolved in a collision, for example).

Alternatively, the longitudinal range may, as in the present exampleembodiment, be determined by evaluating one or more functions that map aset of one or more input parameters or variables relating, for example,to the second model vehicle O to a single output value of thelongitudinal range.

Additionally, or alternatively, the apparatus 10 may, as in the presentexample embodiment, be arranged to determine a respective longitudinalrange for each of the plurality of time instants. Alternatively, theapparatus 10 may be arranged to determine a single longitudinal rangecommon to the plurality of time instants.

Additionally or alternatively, the apparatus 10 may, as in the presentexample embodiment, determine, for each of the plurality of timeinstants, a respective first longitudinal range extending from and aheadof the second model vehicle O and to determine, for each of theplurality of time instants, a respective second longitudinal rangeextending from and behind the second model vehicle O. As such, theregion 50 may be defined such that its longitudinal extent ahead of thesecond model vehicle O differs from its longitudinal extent to the rearof the second model vehicle O. As such, it is may be possible to takeinto account how the respective directions of movement of the first andsecond model vehicles may affect the safe longitudinal distance requiredfor the vehicle 1 to perform a longitudinal emergency manoeuvre such asbraking in time to avoid a collision with the second model vehicle.

By way of example, in example embodiments such as the present exampleembodiment, in which the first vehicle state is further defined by alongitudinal position of the first model vehicle and a longitudinalvelocity of the first model vehicle, and the second vehicle state isfurther defined by a longitudinal velocity of the second model vehicle Oand a longitudinal acceleration of the second model vehicle O, theapparatus 10 may, as in the present example embodiment, determine, foreach of the plurality of time instants, a respective first longitudinalrange extending from and ahead of the second model vehicle O using therespective longitudinal velocity of the first model vehicle, therespective longitudinal velocity of the second model vehicle O, therespective longitudinal acceleration of the second model vehicle O, apredefined reaction time of the second model vehicle O, a firstpredetermined longitudinal deceleration of the second model vehicle O,and a first predetermined longitudinal deceleration of the first modelvehicle. The apparatus 10 may further determine, for each of theplurality of time instants, a respective second longitudinal rangeextending from and behind the second model vehicle O using therespective longitudinal velocity of the first model vehicle, therespective longitudinal velocity of the second model vehicle O, apredefined reaction time of the first model vehicle, a secondpredetermined longitudinal deceleration of the first model vehicle, anda second predetermined longitudinal deceleration of the second modelvehicle O.

By way of example, the first predetermined longitudinal deceleration andthe second predetermined longitudinal deceleration of the second modelvehicle O may, as in the present example embodiment, correspond to aminimum required emergency braking capability and a maximum achievableemergency braking response of the second model vehicle, respectively,such that the first predetermined longitudinal deceleration of thesecond model vehicle O has a smaller magnitude than the secondpredetermined longitudinal deceleration of the second model vehicle O.Additionally, the first predetermined longitudinal deceleration and thesecond predetermined longitudinal deceleration of the first modelvehicle may, as in the present example embodiment, correspond to amaximum achievable emergency braking response and a minimum requiredemergency braking capability of the first model vehicle, respectively,such that the first predetermined longitudinal deceleration of the firstmodel vehicle has a greater magnitude than the second predeterminedlongitudinal deceleration of the first model vehicle.

By way of more detailed example, the apparatus 10 may, as in the presentexample embodiment, determine a respective longitudinal range for eachof the plurality of time instants using the following functions:

$\begin{matrix}{{\Delta{x_{front}\left( {l,v,l_{o},v_{o},a_{o}} \right)}} = {\frac{l_{o}}{2} + \frac{l}{2} + {\max\left( {0,{{\frac{v_{o} + {a_{o}t_{o,r}}}{2}t_{o,r}} + \frac{\left( {v_{o} + {a_{o}t_{o,r}}} \right)^{2}}{{- 2}b_{o,\min}} - \frac{v^{2}}{{- 2}b_{\max}}}} \right)}}} & (9)\end{matrix}$ $\begin{matrix}{{{\Delta{x_{back}\left( {l,v,l_{o},v_{o}} \right)}} = {\frac{l_{o}}{2} + \frac{l}{2} + {\max\left( {0,{{vt}_{r} + {\frac{v^{2}}{{- 2}b_{\min}}\frac{v_{o}^{2}}{{- 2}b_{o,\max}}}}} \right)}}},} & (10)\end{matrix}$

where Δx_(front) corresponds to a safety distance of the vehicle 1 infront of other vehicles, t_(o,r) is a reaction time in seconds (s) ofanother road user, b_(max) is a maximum braking deceleration in ms⁻² ofthe vehicle 1 and b_(o,min) is a minimum emergency braking response inms⁻² of another road user. Furthermore, Δx_(back) corresponds to asafety distance of the vehicle 1 behind other vehicles, t_(r) is areaction (adaptation) time in seconds of the vehicle 1 (s), b_(o,max) isa maximum braking deceleration in ms⁻² of another road user and b_(min)is a minimum emergency braking response (ms⁻²) of the vehicle 1.

In particular, using functions (9) and (19) above, the firstlongitudinal range may be determined as Δx_(front)(l, v_(x), l_(i),v_(x,i), a_(x,i)) and the second longitudinal range may be determined asΔx_(back)(l, v_(x), l_(i), v_(x,i)).

FIG. 6B is a schematic illustration showing an example of the lateralrange 40 determined by the lateral range determining module 13 of theapparatus 10 of FIG. 1 at a particular time instant when the secondmodel vehicle O moves into the lane boundary region 23C. In the exampleof FIG. 6B, the respective lateral range 40 for each of the plurality oftime instants is determined in accordance with equations (6) to (9)above and is depicted by the region 50. However, in line with thediscussion above, in some example embodiments, the region 50 may notactually be determined by the apparatus 10, in which case the region 50may be shown in FIG. 6B for ease of visualization only.

As shown in FIG. 6B, although the second model vehicle O is in the samelane 21C as in FIG. 6A, the extent of the determined lateral range, asillustrated by region 50, increases significantly in the direction oflane 21B into which the second model vehicle O is moving. That is, thelateral ranges 40 reaches past the next lane of the second model vehicleO when it is performing a lane switch such that the first model vehiclemay be prohibited from performing a simultaneous lane switch into thesame lane 21B.

Additionally or alternatively, in example embodiments such as thepresent example embodiment, in which the lateral range determiningmodule 13 determines a left part and a right part of the lateral range40, the lateral range determining module 13 may, as in the presentexample embodiment, determine the respective lateral range 40 for eachof the plurality of time instants such that the lateral extent of thesecond model vehicle O is taken into account.

By way of example, FIG. 6C is a schematic illustration showing a firstexample in which the lateral range determining module 13 determines aleft part and a right part of the lateral range 40 of FIG. 6A. In theexample of FIG. 6C, the left part and the right part of the lateralrange are depicted by regions 51 and 52. However, in line with thediscussion above, in some example embodiments, the regions 51 and 52 maynot actually be determined by the apparatus 10, in which case theseregions may be shown in FIG. 6C for ease of visualization only.

In the example of FIG. 6C, the left part 51 of the lateral range extendsfrom a rightmost edge of the second model vehicle O and to the left ofthe second model vehicle O. Similarly, the right part 52 of the lateralrange extends from a leftmost edge of the second model vehicle O and tothe right of the second model vehicle O. It is noted that the terms‘left’ and ‘right’ may refer more generally to a first lateral directionalong the y-axis, and a second lateral direction, which is opposite tothe first lateral direction, along the y-axis.

As such, in example embodiments such as the present example embodiment,in which the left part of the lateral range is determined asΔy_(range)(y_(i), v_(y,i)) and the right part of the lateral range isdetermined as Δy_(range)(−y_(i), −v_(y,i)) using function 8 above, thefull extent of the left part 51 of the lateral range and the right part52 of the lateral range may be respectively defined by the followingranges:

$\begin{matrix}\left\lbrack {{y_{i} = \frac{w_{o}}{2}},{y_{i} + {\Delta{y_{range}\left( {y_{i},v_{y,i}} \right)}}}} \right\rbrack & (11)\end{matrix}$ $\begin{matrix}{\left\lbrack {{y_{i} - {\Delta{y_{range}\left( {{- y_{i}},{- v_{y,i}}} \right)}}},{y_{i} + \frac{w_{o}}{2}}} \right\rbrack.} & (12)\end{matrix}$

By way of alternative, in example embodiments such as the presentexample embodiment, in which the lateral range determining module 13determines a left part and a right part of the lateral range 40, thelateral range determining module 13 may not take the lateral extent ofthe second model vehicle O into account when determining the respectivelateral range 40 for each of the plurality of time instants.

By way of example, FIG. 6D is a schematic illustration showing a secondexample, in which the lateral range determining module 13 determines aleft part and a right part of the lateral range 40 of FIG. 6A. In theexample of FIG. 6D, the left part and the right part of the lateralrange are depicted by regions 53 and 54. However, in line with thediscussion above, in some example embodiments, the regions 53 and 54 maynot actually be determined by the apparatus 10, in which case theseregions may be shown in FIG. 6D for ease of visualization only.

In the example of FIG. 6D, the left part 53 of the lateral range extendsfrom a lateral centre of the second model vehicle O and to the left ofthe second model vehicle O. Similarly, the right part 54 of the lateralrange extends from a lateral centre of the second model vehicle O and tothe right of the second model vehicle O. It is noted that the terms‘left’ and ‘right’ may refer more generally to a first lateral directionalong the y-axis, and a second lateral direction, which is opposite tothe first lateral direction, along the y-axis.

Additionally, or alternatively, the lateral range determining module 13may, as in the present example embodiment, be further arranged todetermine any other lateral ranges useful in determining the validity ofthe obtained planned trajectory.

By way of example, the lateral range determining module 13 may, as inthe present example embodiment, be further arranged to determine, foreach of the plurality of time instants, a respective second lateralrange extending from the second model vehicle O. The second lateralrange and the second longitudinal range (which may, for example, bedefined using equation (10) above) may, as in the present exampleembodiment, define a braking region of the model of the road extendingin a first lateral direction and in a second lateral direction from alateral centre of the first model vehicle.

The respective second lateral ranges may be determined by any of themeans discussed above in relation to the respective lateral ranges. Therespective second lateral ranges may, as in the present exampleembodiment, be determined using function (8) as described above inrelation to the respective lateral range determined by the lateral rangedetermining module 13.

By way of further example, in example embodiments such as the presentexample embodiment, in which the first vehicle state is further definedby a longitudinal position of the first model vehicle and the secondvehicle state is further defined by a length of the second model vehicleand a width of the second model vehicle, the lateral range determiningmodule 13 may, as in the present example embodiment, determine, for eachof the plurality of time instants, a respective occupancy region whichis occupied by the second model vehicle based on the length of thesecond model vehicle and the width of the second model vehicle. Forexample, the occupancy region may, as in the present example embodiment,correspond to the black rectangle indicated by the reference sign O inFIGS. 2B, and 6A to 6D.

FIG. 7 is a schematic illustration showing an example of the brakingregion 60 determined by the apparatus 10 of FIG. 1 and represents aregion in which the vehicle 1 may be required to perform an emergencybraking response. That is, if the vehicle 1 entered this region, thevehicle 1 may need to apply full emergency braking in order to avoidcrashing in a case where the other road-user in front of the vehicle 1performs an emergency braking response.

Referring again to FIG. 4 , in process step S44 of this Figure, thevalidity determining module 14 determines that the planned trajectory isinvalid in a case where, for the first vehicle state and the secondvehicle state at one or more time instants of the plurality of timeinstants, the following conditions of a first set of conditions aresatisfied:

-   -   (i). the lateral position of the first model vehicle is within        the lateral range 40 of the second model vehicle O at the time        instant and within a lane boundary region 23A, 23B, 23C, 23D        extending along and comprising a lane boundary 22A, 22B, 22C,        22D of the plurality of lane boundaries; and    -   (ii). a direction of the lateral velocity of the first model        vehicle is towards the second model vehicle O and a magnitude of        the lateral acceleration of the first model vehicle away from        the second model vehicle O is less than a predetermined lateral        deceleration of the first model vehicle.

By way of example, the predetermined lateral deceleration may berepresentative of a minimum required lateral deceleration of the vehicle1 (i.e. an acceleration of the first model vehicle away from the secondmodel vehicle O). In such cases, the magnitude of the lateralacceleration of the first model vehicle away from the second modelvehicle O may be less than a predetermined lateral deceleration of thefirst model vehicle in a case where the lateral acceleration of thefirst model vehicle is towards the second model vehicle O and in a casewhere the lateral acceleration of the first model vehicle is away fromthe second model vehicle O, i.e. a deceleration, but the deceleration ofthe first model vehicle is less than the predetermined lateralacceleration.

By way of more specific example, the regions in which condition (i)above is satisfied at a given time instant t may, as in the presentembodiment, be defined as follows for the second model vehicle O (wherethe subscript i denotes that the second model vehicle O may be thei^(th) model vehicle among one or more model vehicles defined in themodel of the road 20 in addition to the first model vehicle):

$\begin{matrix}{{R_{cutl}\left( {H_{t},E_{t}} \right)} = \begin{Bmatrix}\begin{matrix}{\left( {x,y} \right) \in {R_{l}{s.t.x}} \in \left\lbrack {{x_{i} - {\Delta x_{back}\left( {l_{i},v_{x,i},l,v_{x}} \right)}},{x_{i} +}} \right.} \\{\left. {\Delta x_{front}\left( {l_{i},v_{x,i},l,v_{x},a_{x}} \right)} \right\rbrack{and}}\end{matrix} \\{y \in {\left\lbrack {{y_{i} - {\Delta y_{range}\left( {{- y_{i}},{- v_{y,i}}} \right)}},{y_{i} + \frac{w_{o}}{2}}} \right\rbrack{for}{some}O_{i,t}} \in E_{t}}\end{Bmatrix}} & (13)\end{matrix}$ $\begin{matrix}{{{R_{cutr}\left( {H_{t},E_{t}} \right)} = \begin{Bmatrix}{\left( {x,y} \right) \in {R_{l}{s.t.x}} \in \left\lbrack {{x_{i} - {\Delta x_{back}\left( {l_{i},v_{x,i},l,v_{x}} \right)}},{x_{i} +}} \right.} \\\begin{matrix}{\left. {\Delta x_{front}\left( {l_{i},v_{x,i},l,v_{x},a_{x}} \right)} \right\rbrack{and}} \\{y \in {\left\lbrack {{y_{i} - \frac{w_{o}}{2}},{y_{i} + {\Delta y_{range}\left( {y_{i},v_{y,i}} \right)}}} \right\rbrack{for}{some}O_{i,t}} \in E_{t}}\end{matrix}\end{Bmatrix}},} & (14)\end{matrix}$

where R_(cutl) refers to the right part of the lateral range (i.e. thepart intended to prevent the first model vehicle from cutting into asame lane as the second model vehicle O from the right), R_(cutr) refersto the left part of the lateral range (i.e. the part intended to preventthe first model vehicle from cutting into a same lane as the secondmodel vehicle O from the left), R_(l) are the lane boundary regions 23A,23B, 23C, 23D defined in equation (1) above, H_(t) is the first vehiclestate at the time instant t and E_(t) is the state of the environment atthe time instant t. It follows from equations (13) and (14) that theR_(cutl) and R_(cutr) are subsets of the R_(l), and not the entire leftor right part of the lateral range.

Correspondingly, sets of acceptable states H_(t) of the first vehicle,for which condition (ii) above is satisfied at a given time instant t,may, as in the present embodiment, be defined as follows for R_(cutl)and R_(cutr), respectively:P _(cutl) ={H _(t) in H s.t. v _(y)<0 or a _(y) <−b _(y,min)}  (15)P _(cutr) ={H _(t) in H s.t. v _(y)>0 or a _(y) >b _(y,min)},  (16)

where b_(v,min) is the predetermined lateral deceleration.

As described above in relation to FIG. 1A, the process of FIG. 4 mayallow the apparatus 10 to avoid that planned trajectories that representa best response to unsafe driving of another road user are determinedinvalid while ensuring that planned trajectories that may cause thevehicle 1 to be autonomously controlled to drive unsafely may beinvalidated.

Furthermore, by obtaining a first vehicle state and a second vehiclestate for each of the plurality of time instants and determining whetherthe planned trajectory is invalid when conditions (i) and (ii) aresatisfied for even one time instant of the plurality of time instants,the apparatus 10 may allow the safety of the entire planned trajectoryto be analysed.

In some example embodiments, such as the present example embodiment, inwhich the apparatus 10 determines, for each of the plurality of timeinstants, a respective first longitudinal range extending from and aheadof the second model vehicle O and a respective second longitudinal rangeextending from and behind the second model vehicle O, the first set ofconditions may, as in the present example embodiment, further include acondition that the longitudinal position of the first model vehicle isin the first longitudinal range or the second longitudinal range at thetime instant.

Additionally or alternatively, in example embodiments, such as thepresent example embodiment, in which the apparatus 10 determines, foreach of the plurality of time instants, a respective second lateralrange extending from the second model vehicle O, the validitydetermining module 14 may, as in the present example embodiment, befurther configured to determine that the planned trajectory is invalidin a case where, for the first vehicle state and the second vehiclestate for at least one time instant of the plurality of time instants,the following conditions of a second set of conditions are satisfied:

-   -   (i). the longitudinal position of the first model vehicle is        within the second longitudinal range at the time instant,    -   (ii). the lateral position of the first model vehicle is within        the second lateral range at the time instant, and    -   (iii). a magnitude of the longitudinal acceleration of the first        model vehicle away from the second model vehicle is less than        the first predetermined longitudinal deceleration of the first        model vehicle.

By way of example, the first predetermined longitudinal deceleration maybe representative of a minimum required longitudinal deceleration of thevehicle 1 (i.e. an acceleration of the first model vehicle away from thesecond model vehicle O). In such cases, the magnitude of the lateralacceleration of the first model vehicle away from the second modelvehicle O may be less than a predetermined lateral deceleration of thefirst model vehicle in a case where the lateral acceleration of thefirst model vehicle is towards the second model vehicle O and in a casewhere the lateral acceleration of the first model vehicle is away fromthe second model vehicle O, i.e. a deceleration, but the deceleration ofthe first model vehicle is less than the predetermined lateralacceleration.

By way of more specific example, the regions in which conditions (iii)and (iv) above are satisfied at a given time instant t may, as in thepresent embodiment, be defined as follows for the second model vehicle O(where the subscript i denotes that the second model vehicle O may bethe i^(th) model vehicle among one or more model vehicles defined in themodel of the road 20 in addition to the first model vehicle):

$\begin{matrix}{{{R_{b}\left( {H_{t},E_{t}} \right)} = \begin{Bmatrix}{\left( {x,y} \right) \in {R^{2}{s.t.x}} \in {\left\lbrack {{x_{i} - {\Delta{x_{back}\left( {l_{i},v_{x,i},l,v_{x}} \right)}}},x_{i}} \right\rbrack{and}}} \\\begin{matrix}{y \in \left\lbrack {{y_{i} - {\Delta{y_{range}\left( {{- y_{i}},{- v_{y,i}}} \right)}}},{y_{i} + {\Delta{y_{range}\left( {y_{i},v_{y,i}} \right)}}}} \right\rbrack} \\{{{for}{some}O_{i,t}} \in E_{t}}\end{matrix}\end{Bmatrix}},} & (17)\end{matrix}$

where R_(b) refers to the braking region, H_(t) is the first vehiclestate at the time instant t and E_(t) is the state of the environment atthe time instant t.

Correspondingly, sets of acceptable states H_(t) for the first vehicle,for which condition (v) above is satisfied at a given time instant t,may, as in the present embodiment, be defined as follows:P _(b) ={H _(t) in H s.t. a _(x) ≤−b _(min)}  (18)

where b_(min) is the first predetermined longitudinal deceleration.

Accordingly, the second set of conditions may allow the validitydetermining module 14 to determine that the planned trajectory isinvalid in a case where the planned trajectory may cause the vehicle 1to be autonomously controlled to enter the braking region withoutappropriately braking.

Additionally or alternatively, in example embodiments, such as thepresent example embodiment in which the apparatus 10 determines, foreach of the plurality of time instants, a respective occupancy region,the validity determining module 14 may, as in the present exampleembodiment, be further configured to determine that the plannedtrajectory is invalid in a case where, for the first vehicle state andthe second vehicle state for at least one time instant of the pluralityof time instants, the following condition of a third set of conditionsis satisfied:

-   -   (i). the longitudinal position of the first model vehicle and        the lateral position of the first model vehicle are within the        occupancy region occupied by the second model vehicle at the        time instant.

By way of specific example, the regions in which condition (vi) above issatisfied at a given time instant t may, as in the present embodiment,be defined as follows for the second model vehicle O (where thesubscript i denotes that the second model vehicle O may be the i^(th)model vehicle among one or more model vehicles defined in the model ofthe road 20 in addition to the first model vehicle):

$\begin{matrix}{{{R_{o}\left( {H_{t},E_{t}} \right)} = \begin{Bmatrix}{\left( {x,y} \right) \in {R^{2}{s.t.x}} \in {\left\lbrack {{x_{i} - \left( {\frac{1}{2} + \frac{l_{i}}{2}} \right)},{x_{i} + \left( {\frac{1}{2} + \frac{l_{i}}{2}} \right)}} \right\rbrack{and}}} \\{y \in {\left\lbrack {{y_{i} - \left( {\frac{w}{2} + \frac{w_{i}}{2}} \right)},{y_{i} + \left( {\frac{w}{2} + \frac{w_{i}}{2}} \right)}} \right\rbrack{for}{some}O_{i,t}} \in E_{t}}\end{Bmatrix}},} & (19)\end{matrix}$

where H_(t) is the first vehicle state at the time instant t and E_(t)is the state of the environment at the time instant t.

Accordingly, the third set of conditions may allow the validitydetermining module 14 to determine that the planned trajectory isinvalid in a case where the planned trajectory may cause the vehicle 1to collide with a vehicle modeled by the second model vehicle. As thevehicle 1 may never collide with another vehicle, the set of allowedresponses to entering the occupancy region is the empty set. That is,there is no appropriate mitigating response and such trajectories may bedetermined as invalid.

Additionally or alternatively, the validity determining module 14 may,as in the present example embodiment, be further configured to determinethat the planned trajectory is invalid in a case where the lateralposition of the first model vehicle at an initial time instant among theplurality of time instants, and at a last time instant among theplurality of time instants, are located in a common lane of theplurality of lanes and, for the first vehicle state for at least oneintermediate time instant of the plurality of time instants, thefollowing condition of a fourth set of conditions is satisfied:

-   -   (i). the lateral position of the first model vehicle is within a        lane boundary region 23A, 23B, 23C, 23D extending along and        comprising a lane boundary of the common lane at the at least        one intermediate time instant.

By way of example, the at least one intermediate time instant may bebetween the initial time instant and the last time instant.

In particular, as discussed in detail above, the vehicle 1 may only beautonomously controlled to enter the lane boundary regions 23A, 23B,23C, 23D when it is intended to switch lanes. As such, a plannedtrajectory that may cause the vehicle 1 to be autonomously controlled toenter a lane boundary region 23A, 23B, 23C, 23D without resulting in alane switch may be considered unsafe because the first model vehicle maystay near the centre of a lane in which is traveling, in particularwithin a maximal lateral deviation Δy_(bias) from a centre of the lane,unless the first model vehicle is switching lanes.

Accordingly, the fourth set of conditions may allow the validitydetermining module 14 to determine that the planned trajectory isinvalid in a case where the planned trajectory may cause the vehicle 1to enter a lane boundary region 23A, 23B, 23C, 23D in cases where theplanned trajectory does not result in a lane switch.

In example embodiments such as the present example embodiment, in whichthe validity determining module 14 determines whether the plannedtrajectory is valid based on multiple sets of conditions, the validitydetermining module 14 may determine that a planned trajectory is invalidin accordance with one or more of the sets of conditions used. In suchcases, the validity determining module 14 may, as in the present exampleembodiment, be configured to determine that the planned trajectory isinvalid where the planned trajectory is determined to be invalid basedon any of the sets of conditions.

The validity determining module 14 may as in the present exampleembodiment, be configured to determine, in a case where the plannedtrajectory is not determined to be invalid, that the planned trajectoryis a valid planned trajectory.

By way of specific example, the conditions under which the validitydetermining module 14 determines that the planned trajectory is a validplanned trajectory may, as in the present example embodiment, beformally defined as follows:∀t∈T∀s∈S[(x,y)∉R _(s)(H _(t) ,E _(t)) or H _(t) ∈P _(s)],

where S equals o, b, cutl, cutr, T is the plurality of time instants t,H_(t) is the first vehicle state at time instant t, E_(t) is the stateof the environment at time instant t, and (x, y) refers to the positionin the trajectory at time t.

In particular, it is apparent that, in example embodiments such as thepresent example embodiment, in which the validity determining module 14determines whether the planned trajectory is valid based on multiplesets of conditions, the various regions defined by the sets ofconditions may overlap such that a planned trajectory may result in theposition of the first model vehicle lying in two or more regions at oneor more of the plurality of time instants.

FIG. 8 is a schematic illustration showing an example of all regionsdefined by the process of FIG. 4 , in accordance with an exampleembodiment herein. In the Example of FIG. 8 , the lateral range isdepicted by region 50, the braking region is indicated by reference sign60, the occupancy region is indicated by reference sign O, the laneboundary regions are indicated by reference signs 23A, 23B, 23C, 23D andthe regions of overlap between region 50 and the lane boundary regions23A, 23B, 23C, 23D are indicated by reference signs 70 and 71.

In some example embodiments, the process of FIG. 4 may, as in thepresent example embodiment, optionally include a further process step inwhich the validity determining module 14 outputs the valid plannedtrajectory to the automatic driver system 15 so as to enable theautomatic driver system 15 to autonomously control the vehicle to drivealong a road in accordance with the valid planned trajectory.Alternatively, the apparatus 10 may optionally include an additionalmodule configured to output the valid planned trajectory to theautomatic driver system 15.

By way of further alternative, in cases where the apparatus 10 is used,for example, to determine whether trajectories are invalid as part ofsimulation of autonomously controlled vehicles or as part of testing andanalysis of autonomous driving algorithms, such as autonomous drivingalgorithms based on statistical models, the validity determining module14 may be configured to output the valid planned trajectory to anysuitable entity used in the of testing and analysis of autonomousdriving algorithms, such as a connected computing device or a smartphone.

Additionally, or alternatively, in some example embodiments, theapparatus 10 may be arranged to receive multiple planned trajectories,the validity of which may be determined using the process of FIG. 4 . Insuch example embodiments, in cases where no planned trajectory isdetermined to be a valid trajectory, the apparatus 10 may be furtherarranged to output a notification to the entity responsible forgenerating the planned trajectories to prompt a regeneration of aplanned trajectory. Additionally, or alternatively, the apparatus 10 maybe further arranged to output a notification or warning that no validplanned trajectories were determined to any suitable entity.

In the foregoing example embodiments, the first model vehicle and thesecond model vehicle O are each represented as an object having dynamicproperties defined in the lane coordinate system. By way of alternative,the first model vehicle and the second model vehicle may be representedas one or more cells of a grid having dynamic properties defined in thelane coordinate system. By way of example, one or more cells of the gridmay correspond to, for example, a bounding box or other region occupiedby the second model vehicle. As such, the outermost cell or point ineach direction may be considered to define the extent of the boundingbox or other region occupied by the second model vehicle in thatdirection. the first model vehicle and any additional model vehicles maybe defined in the grid in a similar manner.

By way of example, FIGS. 9A and 9B are schematic illustration showing anexample of all regions defined by the process of FIG. 4 for each of afirst cell O_1 and a second cell O_n of a plurality of cellsrepresenting the second model vehicle O. In the example of FIG. 9A, thefirst cell O_1 is the furthest cell in the positive longitudinaldirection (+x) and in the positive lateral direction (+y) of theplurality of cells representing the second model vehicle O and thesecond cell O_n is the furthest cell in the negative longitudinaldirection (−x) and in the negative lateral direction (−y) of theplurality of cells representing the second model vehicle O.

It is noted that the determined lateral range, as well as the otherranges described above in relation to the process of FIG. 4 , aredefined, for example, with respect to a centre of a bounding box of thesecond model vehicle. Alternatively, in example embodiments in which thefirst model vehicle and the second model vehicle are represented as oneor more cells of a grid having dynamic properties defined in the lanecoordinate system, the lateral range determining unit 13 of theapparatus 10 may be configured to determine a respective lateral rangefor some or all of the plurality of cells representing the bounding boxof the second model vehicle O for each of the plurality of timeinstants.

At any given time instant, the union of the respective lateral ranges ofeach of the cells for which a lateral range was calculated may beequivalent to the single lateral range calculated at that time instantin the case where the second model vehicle O is represented as an objecthaving dynamic properties defined in the lane coordinate system. Moreparticularly, the union of the respective lateral ranges of each of thecells for which a lateral range was calculated may be equivalent to thesingle lateral range calculated at that time instant in the case wherethe second model vehicle O is represented as an object having dynamicproperties defined in the lane coordinate system with an error marginthat is dependent on the grid resolution. Accordingly, the lateral rangedetermining unit 13 of the apparatus 10 may be configured to determine asingle lateral range for a given time instant as the union of therespective lateral ranges of each of the cells for which a lateral rangewas calculated for that time instant.

By way of example, in example embodiments such as the present exampleembodiment, in which the lateral range determining unit 13 determinesthe lateral range using function (8) above, it is noted that function(8) is monotonically increasing with the lateral position y_(i) of thesecond model vehicle O for all values of the lateral velocity v_(y,i) ofthe second model vehicle O. As such, the lateral ranges determined forthe intermediate cells of the plurality of cells representing the secondmodel vehicle O will not extend further than the lateral rangesdetermined for the outermost cells. Therefore, the union of the lateralranges the outermost cell points of a given object will be equivalent tothe single lateral range determined at that time instant in the casewhere the second model vehicle O is represented as an object havingdynamic properties defined in the lane coordinate system.

For example, as shown in FIGS. 9A and 9B, the union of the lateralranges (as well as the other ranges and regions) determined for each ofcells O_1 and O_n are equivalent to the single lateral range (as well asthe other ranges and regions) shown in FIG. 8 determined in a case wherethe second model vehicle O is represented as an object having dynamicproperties defined in the lane coordinate system.

The model of the road 20, in which the environment of the first modelvehicle, specifically the first model vehicle and any additional modelvehicles, are represented as one or more cells of a grid having dynamicproperties defined in a suitable coordinate system, may be obtained byany suitable way known to those versed in the art. By way of example,each of the following papers define techniques by which an environmentof a vehicle may be represented as a grid defined in a suitablecoordinate system having occupied cells having dynamic properties:

-   -   Dominik Nuss et al.: “A Random Finite Set Approach for Dynamic        Occupancy Grid Maps with Real-Time Application”,        (arXiv:1605.02406v2);    -   S. Steyer, et al.: “Grid-Based Environment Estimation Using        Evidential Mapping and Particle Tracking,” in IEEE Transactions        on Intelligent Vehicles, vol. 3, no. 3, pp. 384-396, September        2018, doi: 10.1109/TIV.2018.2843130;    -   Stefan Hoermann et al.: “Dynamic Occupancy Grid Prediction for        Urban Autonomous Driving: A Deep Learning Approach with Fully        Automatic Labeling”, (arXiv:1705.08781v2); and    -   Christopher Diehl et al.: “Radar-based Dynamic Occupancy Grid        Mapping and Object Detection”, (arXiv:2008.03696v1).

The example aspects described here avoid limitations, specificallyrooted in computer technology, relating to the field of autonomousdriving. By virtue of the example aspects described herein, it can beavoided that planned trajectories that represent a best response tounsafe driving of another road user are determined invalid, whileensuring that planned trajectories that may cause a vehicle to beautonomously controlled to drive unsafely may be invalidated.Furthermore, by obtaining a first vehicle state and a second vehiclestate for each of the plurality of time instants and determining whetherthe planned trajectory is invalid when at least the first set ofconditions are satisfied for even one time instant of the plurality oftime instants, the techniques herein may allow the safety of the entireplanned trajectory to be analysed. In some example embodiments, such asthe present example embodiment, in which the apparatus 10 determines,for each of the plurality of time instants, a respective firstlongitudinal range extending from and ahead of the second model vehicleO and a respective second longitudinal range extending from and behindthe second model vehicle O, the first set of conditions may, as in thepresent example embodiment, further comprise a condition that thelongitudinal position of the first model vehicle is in the firstlongitudinal range or the second longitudinal range at the time instant.Also, by virtue of the foregoing capabilities of the example aspectsdescribed herein, which are rooted in computer technology, the exampleaspects described herein improve computers and computerprocessing/functionality, and also improve the field(s) of at least ofautonomous driving and, in particular, determination of whether aplanned trajectory of a first model vehicle, for use in autonomouscontrol of a vehicle modeled by the first model vehicle, is invalid.

In the foregoing description, aspects are described with reference toseveral embodiments. Accordingly, the specification should be regardedas illustrative, rather than restrictive. Similarly, the figuresillustrated in the drawings, which highlight the functionality andadvantages of the embodiments, are presented for example purposes only.The architecture of the embodiments is sufficiently flexible andconfigurable, such that it may be utilized in ways other than thoseshown in the accompanying figures.

Software embodiments presented herein may be provided as a computerprogram, or software, such as one or more programs having instructionsor sequences of instructions, included or stored in an article ofmanufacture such as a machine-accessible or machine-readable medium, aninstruction store, or computer-readable storage device, each of whichcan be non-transitory, in one example embodiment. The program orinstructions on the non-transitory machine-accessible medium,machine-readable medium, instruction store, or computer-readable storagedevice, may be used to program a computer system or other electronicdevice. The machine- or computer-readable medium, instruction store, andstorage device may include, but are not limited to, floppy diskettes,optical disks, and magneto-optical disks or other types ofmedia/machine-readable medium/instruction store/storage device suitablefor storing or transmitting electronic instructions. The techniquesdescribed herein are not limited to any particular softwareconfiguration. They may find applicability in any computing orprocessing environment. The terms “computer-readable”,“machine-accessible medium”, “machine-readable medium”, “instructionstore”, and “computer-readable storage device” used herein shall includeany medium that is capable of storing, encoding, or transmittinginstructions or a sequence of instructions for execution by the machine,computer, or computer processor and that causes themachine/computer/computer processor to perform any one of the methodsdescribed herein. Furthermore, it is common in the art to speak ofsoftware, in one form or another (e.g., program, procedure, process,application, module, unit, logic, and so on), as taking an action orcausing a result. Such expressions are merely a shorthand way of statingthat the execution of the software by a processing system causes theprocessor to perform an action to produce a result.

Some embodiments may also be implemented by the preparation ofapplication-specific integrated circuits, field-programmable gatearrays, or by interconnecting an appropriate network of conventionalcomponent circuits.

Some embodiments include a computer program product. The computerprogram product may be a storage medium or media, instruction store(s),or storage device(s), having instructions stored thereon or thereinwhich can be used to control, or cause, a computer or computer processorto perform any of the procedures of the example embodiments describedherein. The storage medium/instruction store/storage device may include,by example and without limitation, an optical disc, a ROM, a RAM, anEPROM, an EEPROM, a DRAM, a VRAM, a flash memory, a flash card, amagnetic card, an optical card, nano systems, a molecular memoryintegrated circuit, a RAID, remote data storage/archive/warehousing,and/or any other type of device suitable for storing instructions and/ordata.

Stored on any one of the computer-readable medium or media, instructionstore(s), or storage device(s), some implementations include softwarefor controlling both the hardware of the system and for enabling thesystem or microprocessor to interact with a human user or othermechanism utilizing the results of the embodiments described herein.Such software may include without limitation device drivers, operatingsystems, and user applications. Ultimately, such computer-readable mediaor storage device(s) further include software for performing exampleaspects, as described above.

Included in the programming and/or software of the system are softwaremodules for implementing the procedures described herein. In someexample embodiments herein, a module includes software, although inother example embodiments herein, a module includes hardware, or acombination of hardware and software.

While various embodiments of the present disclosure have been describedabove, it should be understood that they have been presented by way ofexample, and not limitation. It will be apparent to persons skilled inthe relevant art(s) that various changes in form and detail can be madetherein. Thus, the present disclosure should not be limited by any ofthe above described example embodiments but should be defined only inaccordance with the following claims and their equivalents.

Further, the purpose of the Abstract is to enable the Patent Office andthe public generally, and especially the scientists, engineers andpractitioners in the art who are not familiar with patent or legal termsor phraseology, to determine quickly from a cursory inspection thenature and essence of the technical disclosure of the application. TheAbstract is not intended to be limiting as to the scope of theembodiments presented herein in any way. It is also to be understoodthat any procedures recited in the claims need not be performed in theorder presented.

While this specification contains many specific embodiment details,these should not be construed as limitations on what may be claimed, butrather as descriptions of features specific to particular embodimentsdescribed herein. Certain features that are described in thisspecification in the context of separate embodiments can also beimplemented in combination in a single embodiment. Conversely, variousfeatures that are described in the context of a single embodiment canalso be implemented in multiple embodiments separately or in anysuitable sub-combination. Moreover, although features may be describedabove as acting in certain combinations and even initially claimed assuch, one or more features from a claimed combination can in some casesbe excised from the combination, and the claimed combination may bedirected to a sub-combination or variation of a sub-combination.

In certain circumstances, multitasking and parallel processing may beadvantageous. Moreover, the separation of various components in theembodiments described above should not be understood as requiring suchseparation in all embodiments, and it should be understood that thedescribed program components and systems can generally be integratedtogether in a single software product or packaged into multiple softwareproducts.

Having described some illustrative embodiments, it is apparent that theforegoing is illustrative and not limiting, having been presented by wayof example. In particular, although many of the examples presentedherein involve specific combinations of apparatus or software elements,those elements may be combined in other ways to accomplish the sameobjectives. Acts, elements, and features discussed only in connectionwith one embodiment are not intended to be excluded from a similar rolein other embodiments or embodiments.

The apparatuses described herein may be embodied in other specific formswithout departing from the characteristics thereof. The foregoingembodiments are illustrative rather than limiting of the describedsystems and methods. Scope of the apparatuses described herein is thusindicated by the appended claims, rather than the foregoing description,and changes that come within the meaning and range of equivalence of theclaims are embraced therein.

What is claimed is:
 1. A method of determining whether a plannedtrajectory of a first model vehicle is invalid, the method comprising:obtaining the planned trajectory, the planned trajectory: correspondingto a model of a road along which the first model vehicle and a secondmodel vehicle are traveling, the model of the road comprising aplurality of lanes defined by a plurality of lane boundaries, usable forautonomous control of a vehicle modelled as the first model vehicle, andcomprising, for each of a plurality of time instants, a first vehiclestate of the first model vehicle defined relative to the model of theroad at the respective time instant, the first vehicle state comprising:a lateral position of the first model vehicle, a lateral velocity of thefirst model vehicle, and a lateral acceleration of the first modelvehicle at the respective time instant; obtaining, for each of theplurality of time instants, a second vehicle state of the second modelvehicle defined relative to the model of the road at the respective timeinstant, the second vehicle state comprising a lateral position of thesecond model vehicle in the model of the road at the respective timeinstant; determining, for each of the plurality of time instants, alateral range extending from the second model vehicle at the respectivetime instant, the lateral range based on the lateral position of thesecond model vehicle relative to a center of a lane of the plurality oflanes in which the second model vehicle is located at the respectivetime instant; determining that the planned trajectory is invalidresponsive to determining, for at least one of the time instants, that:the lateral position of the first model vehicle is within the lateralrange of the second model vehicle and within a lane boundary region thatextends along and comprises one of the lane boundaries, and the lateralvelocity of the first model vehicle is towards the second model vehicle,and the lateral acceleration of the first model vehicle is away from thesecond model vehicle and a magnitude of the lateral acceleration of thefirst model vehicle away from the second model vehicle is less than amagnitude of a predetermined lateral deceleration of the first modelvehicle; and responsive to determining that the planned trajectory isvalid for each of the time instants, controlling operation of the firstmodel vehicle along the planned trajectory; or responsive to determiningthat the planned trajectory is invalid for at least one of the timeinstants, causing another planned trajectory of the first model vehicleto be generated.
 2. The method according to claim 1, wherein: the secondvehicle state further comprises a lateral velocity of the second modelvehicle; and the lateral range is based on the lateral velocity of thesecond model vehicle.
 3. The method according to claim 1, wherein: thefirst vehicle state further comprises a longitudinal position of thefirst model vehicle and a longitudinal velocity of the first modelvehicle; the second vehicle state further comprises a longitudinalvelocity of the second model vehicle and a longitudinal acceleration ofthe second model vehicle; and the method further comprises: determining,for each of the plurality of time instants, a first longitudinal rangeat the respective time instant, the first longitudinal range extendingfrom and ahead of the second model vehicle and being based on: thelongitudinal velocity of the first model vehicle, the longitudinalvelocity of the second model vehicle, the longitudinal acceleration ofthe second model vehicle, a predefined reaction time of the second modelvehicle, a first predetermined longitudinal deceleration of the secondmodel vehicle, and a first predetermined longitudinal deceleration ofthe first model vehicle at the respective time instant; and determining,for each of the plurality of time instants, a second longitudinal rangeat the respective time instant, the second longitudinal range extendingfrom and behind the second model vehicle and being based on: thelongitudinal velocity of the first model vehicle, the longitudinalvelocity of the second model vehicle, a predefined reaction time of thefirst model vehicle, a second predetermined longitudinal deceleration ofthe first model vehicle, and a second predetermined longitudinaldeceleration of the second model vehicle at the respective time instant.4. The method according to claim 3, wherein the determining that theplanned trajectory is invalid is further responsive to determining thatthe longitudinal position of the first model vehicle is in the firstlongitudinal range or the second longitudinal range for at least one ofthe time instants.
 5. The method according to claim 3, furthercomprising: determining, for each of the plurality of time instants, asecond lateral range at the respective time instant, the second lateralrange extending from the second model vehicle, wherein the secondlateral range and the second longitudinal range define a braking regionof the model of the road extending in a first lateral direction and in asecond lateral direction from a lateral center of the first modelvehicle; and determining that the planned trajectory is invalidresponsive to determining, for at least one of the time instants that:the longitudinal position of the first model vehicle is within thesecond longitudinal range, the lateral position of the first modelvehicle is within the second lateral range, and the longitudinalacceleration of the first model vehicle is away from the second modelvehicle and is less than the first predetermined longitudinaldeceleration of the first model vehicle.
 6. The method according toclaim 1, wherein: the first vehicle state further comprises alongitudinal position of the first model vehicle; the second vehiclestate further comprises a length of the second model vehicle and a widthof the second model vehicle; and the method further comprises:determining, for each of the plurality of time instants, an occupancyregion that is occupied by the second model vehicle, the occupancyregion being based on the length of the second model vehicle and thewidth of the second model vehicle at the respective time instant; anddetermining that the planned trajectory is invalid responsive todetermining, for at least one of the time instants that the longitudinalposition of the first model vehicle and the lateral position of thefirst model vehicle are within the occupancy region occupied by thesecond model vehicle.
 7. The method according to claim 1, wherein thesecond model vehicle comprises: a location of the second model vehiclein a lane coordinate system of the model of the road, a length of thesecond model vehicle along a longitudinal axis of the lane coordinatesystem, and a width of the second model vehicle along a lateral axis ofthe lane coordinate system; or one or more cells of a grid defined inthe lane coordinate system.
 8. The method according to claim 1, furthercomprising: determining that the planned trajectory is invalidresponsive to determining: for an initial time instant and a last timeinstant of the time instants, that the lateral position of the firstmodel vehicle is within a common lane of the plurality of lanes; and foran intermediate time instant of the time instants, that the lateralposition of the first model vehicle is within a lane boundary regionextending along and comprising a lane boundary of the common lane. 9.The method according to claim 1, wherein a time interval between eachsuccessive pair of the time instants is less than or equal to apredefined reaction time of the first model vehicle.
 10. The methodaccording to claim 1, further comprising: determining that the plannedtrajectory is valid responsive to not determining that: the lateralposition of the first model vehicle is within the lateral range of thesecond model vehicle and within the lane boundary region that extendsalong and comprises one of the lane boundaries, that the lateralvelocity of the first model vehicle is towards the second model vehicle,and that the lateral acceleration of the first model vehicle is awayfrom the second model vehicle and is less than the predetermined lateraldeceleration of the first model vehicle; and outputting the plannedtrajectory to an automatic driver system effective to enable theautomatic driver system to autonomously control the vehicle to drivealong the road in accordance with the planned trajectory.
 11. Anon-transitory computer-readable storage medium comprising instructionsthat, when executed by a computer processor, cause the computerprocessor to: obtain a planned trajectory, the planned trajectory:corresponding to a model of a road along which a first model vehicle anda second model vehicle are traveling, the model of the road comprising aplurality of lanes defined by a plurality of lane boundaries, usable forautonomous control of a vehicle modelled as the first model vehicle, andcomprising, for each of a plurality of time instants, a first vehiclestate of the first model vehicle defined relative to the model of theroad at the respective time instant, the first vehicle state comprising:a lateral position of the first model vehicle, a lateral velocity of thefirst model vehicle, and a lateral acceleration of the first modelvehicle at the respective time instant; obtain, for each of theplurality of time instants, a second vehicle state of the second modelvehicle defined relative to the model of the road at the respective timeinstant, the second vehicle state comprising a lateral position of thesecond model vehicle in the model of the road at the respective timeinstant; determine, for each of the plurality of time instants, alateral range extending from the second model vehicle at the respectivetime instant, the lateral range based on the lateral position of thesecond model vehicle relative to a center of a lane of the plurality oflanes in which the second model vehicle is located at the respectivetime instant; determine that the planned trajectory is invalidresponsive to determining, for at least one of the time instants, that:the lateral position of the first model vehicle is within the lateralrange of the second model vehicle and within a lane boundary region thatextends along and comprises one of the lane boundaries, and the lateralvelocity of the first model vehicle is towards the second model vehicle,and the lateral acceleration of the first model vehicle is away from thesecond model vehicle and a magnitude of the lateral acceleration of thefirst model vehicle away from the second model vehicle is less than amagnitude of a predetermined lateral deceleration of the first modelvehicle; and responsive to a determination that the planned trajectoryis valid for each of the time instants, control operation of the firstmodel vehicle along the planned trajectory; or responsive to adetermination that the planned trajectory is invalid for at least one ofthe time instants, cause another planned trajectory of the first modelvehicle to be generated.
 12. An apparatus comprising a computerprocessor configured to: obtain a planned trajectory, the plannedtrajectory: corresponding to a model of a road along which a first modelvehicle and a second model vehicle are traveling, the model of the roadcomprising a plurality of lanes defined by a plurality of laneboundaries, usable for autonomous control of a vehicle modelled as thefirst model vehicle, and comprising, for each of a plurality of timeinstants, a first vehicle state of the first model vehicle definedrelative to the model of the road at the respective time instant, thefirst vehicle state comprising: a lateral position of the first modelvehicle, a lateral velocity of the first model vehicle, and a lateralacceleration of the first model vehicle at the respective time instant;obtain, for each of the plurality of time instants, a second vehiclestate of the second model vehicle defined relative to the model of theroad at the respective time instant, the second vehicle state comprisinga lateral position of the second model vehicle in the model of the roadat the respective time instant; determine, for each of the plurality oftime instants, a lateral range extending from the second model vehicleat the respective time instant, the lateral range based on the lateralposition of the second model vehicle relative to a center of a lane ofthe plurality of lanes in which the second model vehicle is located atthe respective time instant; determine that the planned trajectory isinvalid responsive to determining, for at least one of the timeinstants, that: the lateral position of the first model vehicle iswithin the lateral range of the second model vehicle and within a laneboundary region that extends along and comprises one of the laneboundaries, the lateral velocity of the first model vehicle is towardsthe second model vehicle, and the lateral acceleration of the firstmodel vehicle is away from the second model vehicle and a magnitude ofthe lateral acceleration of the first model vehicle away from the secondmodel vehicle is less than a magnitude of a predetermined lateraldeceleration of the first model vehicle; and responsive to adetermination that the planned trajectory is valid for each of the timeinstants, control operation of the first model vehicle along the plannedtrajectory; or responsive to a determination that the planned trajectoryis invalid for at least one of the time instants, cause another plannedtrajectory of the first model vehicle to be generated.
 13. The apparatusof claim 12, wherein: the second vehicle state further comprises alateral velocity of the second model vehicle; and the lateral range isbased on the lateral velocity of the second model vehicle.
 14. Theapparatus of claim 12, wherein: the first vehicle state furthercomprises a longitudinal position of the first model vehicle and alongitudinal velocity of the first model vehicle; the second vehiclestate further comprises a longitudinal velocity of the second modelvehicle and a longitudinal acceleration of the second model vehicle; andthe processor is further configured to: determine, for each of theplurality of time instants, a first longitudinal range at the respectivetime instant, the first longitudinal range extending from and ahead ofthe second model vehicle and being based on: the longitudinal velocityof the first model vehicle, the longitudinal velocity of the secondmodel vehicle, the longitudinal acceleration of the second modelvehicle, a predefined reaction time of the second model vehicle, a firstpredetermined longitudinal deceleration of the second model vehicle, anda first predetermined longitudinal deceleration of the first modelvehicle at the respective time instant; determine, for each of theplurality of time instants, a second longitudinal range at therespective time instant, the second longitudinal range extending fromand behind the second model vehicle and being based on: the longitudinalvelocity of the first model vehicle, the longitudinal velocity of thesecond model vehicle, a predefined reaction time of the first modelvehicle, a second predetermined longitudinal deceleration of the firstmodel vehicle, and a second predetermined longitudinal deceleration ofthe second model vehicle at the respective time instant; and determinethat the planned trajectory is invalid responsive to determining thatthe longitudinal position of the first model vehicle is in the firstlongitudinal range or the second longitudinal range for at least one ofthe time instants.
 15. The apparatus of claim 14, wherein the processoris further configured to: determine, for each of the plurality of timeinstants, a second lateral range at the respective time instant, thesecond lateral range extending from the second model vehicle, whereinthe second lateral range and the second longitudinal range define abraking region of the model of the road extending in a first lateraldirection and in a second lateral direction from a lateral center of thefirst model vehicle; and determine that the planned trajectory isinvalid responsive to determining, for at least one of the time instantsthat: the longitudinal position of the first model vehicle is within thesecond longitudinal range, the lateral position of the first modelvehicle is within the second lateral range, and the longitudinalacceleration of the first model vehicle is away from the second modelvehicle and is less than the first predetermined longitudinaldeceleration of the first model vehicle.
 16. The apparatus of claim 12,wherein: the first vehicle state further comprises a longitudinalposition of the first model vehicle; the second vehicle state furthercomprises a length of the second model vehicle and a width of the secondmodel vehicle; and the processor is further configured to: determine,for each of the plurality of time instants, an occupancy region that isoccupied by the second model vehicle, the occupancy region being basedon the length of the second model vehicle and the width of the secondmodel vehicle at the respective time instant; and determine that theplanned trajectory is invalid responsive to determining, for at leastone of the time instants that the longitudinal position of the firstmodel vehicle and the lateral position of the first model vehicle arewithin the occupancy region occupied by the second model vehicle. 17.The apparatus of claim 12, wherein the second model vehicle comprises: alocation of the second model vehicle in a lane coordinate system of themodel of the road, a length of the second model vehicle along alongitudinal axis of the lane coordinate system, and a width of thesecond model vehicle along a lateral axis of the lane coordinate system;or one or more cells of a grid defined in the lane coordinate system.18. The apparatus of claim 12, wherein the processor is furtherconfigured to: determine that the planned trajectory is invalidresponsive to determining: for an initial time instant and a last timeinstant of the time instants, that the lateral position of the firstmodel vehicle is within a common lane of the plurality of lanes; and foran intermediate time instant of the time instants, that the lateralposition of the first model vehicle is within a lane boundary regionextending along and comprising a lane boundary of the common lane. 19.The apparatus of claim 12, wherein a time interval between eachsuccessive pair of the time instants is less than or equal to apredefined reaction time of the first model vehicle.
 20. The apparatusof claim 12, wherein the processor is further configured to: determinethat the planned trajectory is valid responsive to not determining that:the lateral position of the first model vehicle is within the lateralrange of the second model vehicle and within the lane boundary regionthat extends along and comprises one of the lane boundaries, that thelateral velocity of the first model vehicle is towards the second modelvehicle, and that the lateral acceleration of the first model vehicle isaway from the second model vehicle and is less than the predeterminedlateral deceleration of the first model vehicle; and output the plannedtrajectory to an automatic driver system effective to enable theautomatic driver system to autonomously control the vehicle to drivealong the road in accordance with the planned trajectory.